SSC CHSL Tier 1 2024 Quantitative Aptitude Questions with Solutions

Explanation

Using the work formula, the rate of work is given by: 1/A + 1/B = 1/Total

Here, the combined time of A and B is 8 days, and B's individual time is 16 days. Substituting these values into the formula: 1/A + 1/16 = 1/8

Subtracting 1/16 from both sides: 1/A = 1/8 - 1/16 1/A = (2 - 1)/16 1/A = 1/16

Thus, A alone can complete the piece of work in 16 days.

Explanation

The total marks for the examination are 50. To be eligible for higher studies in Physics, a student must obtain at least 60% of the total marks.

Required minimum marks = 60% of 50 = (60 / 100) × 50 = 30 marks

From the given table, the row for Physics shows the cumulative number of students who scored marks within different ranges. The number of students who scored 30 or above in Physics is 21. Thus, there are 21 students eligible to pursue higher studies in Physics.

Explanation

Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit. The number obtained by interchanging the digits is 10y + x.

According to the question, the sum of the two numbers is 77: (10x + y) + (10y + x) = 77 11x + 11y = 77 x + y = 7

The difference between the digits is 1: |x - y| = 1

Solving these two equations: If x - y = 1: Adding x + y = 7 and x - y = 1 gives 2x = 8, which means x = 4 and y = 3. This gives the number 43.

If y - x = 1: Adding x + y = 7 and y - x = 1 gives 2y = 8, which means y = 4 and x = 3. This gives the number 34.

Checking the given choices, the number 34 satisfies all the conditions.

Explanation

The difference in simple interest for the same principal sum at a constant rate of interest is directly proportional to the difference in time periods.

Using the simple interest formula, Simple Interest = Principal × Rate × Time / 100.

The difference in interest paid by P and Q is: Difference in Interest = (Principal × Rate × (T₂ - T₁)) / 100

Substituting the given values: 172 = (Principal × 8.6 × (8 - 7)) / 100 172 = Principal × 8.6 / 100 172 = Principal × 0.086 Principal = 172 / 0.086 Principal = 2000

Thus, the sum lent to each was ₹2,000.

Explanation

The volume of the copper remains constant when it is drawn from a sphere into a cylindrical wire.

Volume of sphere = Volume of cylindrical wire 4/3 π R³ = π r² h

The radius of the sphere R is 9 cm, and the radius of the wire r is 4 mm, which is equal to 0.4 cm. Substituting these values into the formula:

4/3 × 9³ = 0.4² × h 4/3 × 729 = 0.16 × h 4 × 243 = 0.16 × h 972 = 0.16 × h h = 972 / 0.16 h = 6075 cm

To convert the length from centimeters to meters, divide by 100: h = 60.75 m

Explanation

The perpendicular drawn from the centre of a circle to a chord bisects the chord.

For a chord of length 12 units, the perpendicular divides it into two segments of 6 units each. This perpendicular distance d, the half-chord length of 6 units, and the radius of 10 units form a right-angled triangle.

Applying Pythagoras' theorem: d² + 6² = 10² d² + 36 = 100 d² = 64 d = 8

The distance of the chord from the centre is 8 units.

Explanation

Using the deviation method, when the supervisor is excluded, the average age of the remaining 24 workers decreases by 0.75 years. This indicates that the supervisor's age is greater than the initial average of 41 by the total sum of the decrease distributed across the remaining 24 workers.

Supervisor's age = Original average + (Decrease in average × Remaining number of workers)

Substituting the given values: Supervisor's age = 41 + (0.75 × 24) Supervisor's age = 41 + 18 Supervisor's age = 59 years

Alternatively, using the total sum method: Total age of 25 people = 25 × 41 = 1025 years New average age of 24 workers = 41 - 0.75 = 40.25 years Total age of 24 workers = 24 × 40.25 = 966 years Supervisor's age = 1025 - 966 = 59 years

Explanation

According to the tangent-secant theorem, when a tangent segment and a secant segment are drawn to a circle from an exterior point, the square of the length of the tangent segment is equal to the product of the lengths of the external secant segment and the entire secant segment.

Applying this theorem to the given circle: XR² = QR × PR

The total length of the secant segment PR is the sum of PQ and QR: PR = PQ + QR = x + (x - 2) = 2x - 2

Substituting the given values into the relation: 12² = (x - 2)(2x - 2) 144 = 2(x - 2)(x - 1) 72 = (x - 2)(x - 1) 72 = x² - 3x + 2 x² - 3x - 70 = 0 (x - 10)(x + 7) = 0

Solving for x gives x = 10 or x = -7. Since the length of a segment must be positive, we discard the negative value. Thus, the value of x is 10 cm.

Explanation

To find the ratio M : N : O from the given ratio of their reciprocals, we take the reciprocal of each term:

M : N : O = 1/3 : 1/4 : 1/5

To convert this fractional ratio into integers, we multiply each term by the Least Common Multiple (LCM) of the denominators 3, 4, and 5. The LCM of 3, 4, and 5 is 60.

Multiplying each part of the ratio by 60:

M : N : O = (1/3 × 60) : (1/4 × 60) : (1/5 × 60)

M : N : O = 20 : 15 : 12

Explanation

In a right-angled triangle, sin θ is the ratio of the perpendicular to the hypotenuse.

sin θ = perpendicular / hypotenuse = 2xy / (x² + y²)

By setting perpendicular P = 2xy and hypotenuse H = x² + y², the base B is calculated using the Pythagorean theorem:

B = √(H² - P²) B = √((x² + y²)² - (2xy)²) B = √(x⁴ + 2x²y² + y⁴ - 4x²y²) B = √(x⁴ - 2x²y² + y⁴) B = √((x² - y²)²) B = x² - y²

The trigonometric ratio for tan θ is the ratio of the perpendicular to the base:

tan θ = P / B = 2xy / (x² - y²)

Explanation

The total percentage of votes cast in the election is 100%. The winning candidate gets 72% of the total votes, which means the losing candidate gets the remaining portion of the votes: 100% - 72% = 28%

The margin of victory is the difference in the percentage of votes received by the two candidates: 72% - 28% = 44%

Given that the total number of votes cast is 1000, the margin of victory in terms of votes is: 44% of 1000 = 0.44 × 1000 = 440

Explanation

According to the divisibility rule for 3, a number is divisible by 3 if the sum of its digits is divisible by 3.

Let the digit in the blank space be x. The sum of the digits of the number 7x7624 is: 7 + x + 7 + 6 + 2 + 4 = 26 + x

For the number to be divisible by 3, the sum (26 + x) must be a multiple of 3. The smallest multiple of 3 that is greater than or equal to 26 is 27.

Setting the sum equal to 27 gives: 26 + x = 27 x = 1

Thus, the smallest digit that can be placed in the blank space to make the number divisible by 3 is 1.

Explanation

The successive percentage change formula for an increase of a% followed by a decrease of b% is:

Net percentage change = a - b - (a × b)/100

Substituting a = 44 and b = 30 into the formula:

Net percentage change = 44 - 30 - (44 × 30)/100 Net percentage change = 14 - 13.2 = 0.8%

Rounding 0.8% to the nearest integer gives 1%. Since the value is positive, it represents an increase.

Explanation

Total pizzas sold by bakeries Y and Z together in November: 104 + 106 = 210

Total pizzas sold by bakeries X and W together in November: 120 + 105 = 225

The required ratio of Y and Z together to X and W together in November: 210 : 225

Dividing both terms by their common factor of 5: 210 ÷ 5 = 42 225 ÷ 5 = 45

This simplifies to the ratio of 42 : 45.

Explanation

The area of a triangle is given by the formula: Area = ½ × base × height

Let the height of the triangle be h cm. The base is given as two-thirds of its height, which is ⅔h.

Substituting these values into the area formula: 363 = ½ × ⅔h × h 363 = ⅓h²

Multiplying both sides by 3 to solve for h²: h² = 363 × 3 h² = 1089

Taking the square root of both sides: h = √1089 h = 33 cm

Explanation

For a constant distance, speed and time are inversely proportional. This relationship is represented by the formula:

s₁ × t₁ = s₂ × t₂

Here, the initial speed s₁ is 60 km/h and the initial time t₁ is 45 minutes. The required time t₂ is 30 minutes. Let the required speed be s₂.

Substituting these values into the formula:

60 × 45 = s₂ × 30

s₂ = (60 × 45) / 30

s₂ = 90 km/h

Explanation

Correct Answer: C

To find the net gain percentage, use the successive percentage formula:

Net Gain = m - d - (m × d) / 100

where m is the markup percentage and d is the discount percentage.

Substituting the given values, m = 32 and d = 21:

Net Gain = 32 - 21 - (32 × 21) / 100 Net Gain = 11 - 672 / 100 Net Gain = 11 - 6.72 Net Gain = 4.28%

Explanation

Using the weighted average method for profit and loss, let the total quantity of watermelons be 4 units.

One-fourth of the quantity is 1 unit, which is sold at a loss of 12% (represented as -12%). The remaining quantity is 3 units, sold at a gain of x%. The overall gain on the entire 4 units is 25%.

The weighted average relation is: Total Gain = (Quantity 1 × Profit 1) + (Quantity 2 × Profit 2) 4 × 25 = 1 × (-12) + 3 × x 100 = -12 + 3x 3x = 112 x = 112 / 3 ≈ 37.33%

The remaining watermelons must be sold at a gain of 37.33% to achieve the desired overall profit.

Explanation

The time taken by two individuals working together to complete a task is given by the formula:

T = (a × b) / (a + b)

where a and b are the times taken by each individual to complete the task alone.

Here, Shobhita's time a = 20 hours and Saroj's time b = 15 hours.

Substituting these values into the formula:

T = (20 × 15) / (20 + 15) T = 300 / 35 T = 60 / 7 T = 8 4/7 hours

Explanation

For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides:

Area(ΔABC) / Area(ΔDEF) = (BC / EF)²

Substituting the given values into the formula:

0.64 / 0.0121 = (BC / 0.154)²

Taking the square root on both sides:

0.8 / 0.11 = BC / 0.154

Solving for BC:

BC = (0.8 × 0.154) / 0.11 BC = 0.8 × 1.4 BC = 1.12 m

Explanation

The curved surface area (CSA) of a cylinder is given by the formula:

CSA = 2πrh

The radius (r) is half of the diameter:

r = 28 / 2 = 14 cm

The height (h) of the cylinder is 42 cm. Using π = 22/7, substitute these values into the formula:

CSA = 2 × (22/7) × 14 × 42 CSA = 2 × 22 × 2 × 42 CSA = 3696 cm²

Explanation

Let the two concentric circles have center O. The radius of the larger circle is R = 35 cm, and the radius of the smaller circle is r = 21 cm.

Let AB be the chord of the larger circle that is tangent to the smaller circle at point P. The radius OP is perpendicular to the tangent chord AB at the point of contact P. This forms a right-angled triangle OPA, where OA is the hypotenuse.

Using Pythagoras' theorem in triangle OPA: AP² = OA² - OP² AP² = 35² - 21² AP² = 1225 - 441 AP² = 784 AP = √784 = 28 cm

Since the perpendicular from the center of a circle to a chord bisects the chord, P is the midpoint of AB.

Therefore, the length of the chord AB is: AB = 2 × AP = 2 × 28 = 56 cm

Explanation

Expanding the terms in the numerator using the given identity:

sin(A - B) / (cos A cos B) = (sin A cos B - cos A sin B) / (cos A cos B) = tan A - tan B

Similarly, the second term simplifies as:

sin(B - C) / (cos B cos C) = (sin B cos C - cos B sin C) / (cos B cos C) = tan B - tan C

Adding these two simplified expressions gives:

(tan A - tan B) + (tan B - tan C) = tan A - tan C

Converting tan A - tan C back to sine and cosine forms:

tan A - tan C = (sin A / cos A) - (sin C / cos C) = (sin A cos C - cos A sin C) / (cos A cos C) = sin(A - C) / (cos A cos C)

Explanation

By trigonometric co-function identity, cot(90 - θ) = tan θ.

Given cos θ = 24/25 for an acute angle θ. In a right-angled triangle, the cosine of an angle is the ratio of the base to the hypotenuse.

Applying the Pythagorean theorem to find the perpendicular: Perpendicular = √(Hypotenuse² - Base²) = √(25² - 24²) = √(625 - 576) = √49 = 7

Using the definition of tangent: tan θ = Perpendicular / Base = 7/24

Therefore, cot(90 - θ) = 7/24.

Explanation

Let the initial number of toffees with R and S be equal to T.

Since R gives 2/3 of his toffees to S: Toffees given to S = 2/3 T

Toffees remaining with R = T - 2/3 T = 1/3 T

New number of toffees with S = T + 2/3 T = 5/3 T

The number of toffees now with S is k% of the toffees originally with R: 5/3 T = (k/100) × T

Solving for k: k/100 = 5/3 k = 500/3

Explanation

To find the number of valid votes polled in favour of the candidate, we calculate the percentage step-by-step from the total number of voters.

Total number of voters = 2,40,000

Since 3% of the total votes were invalid, the percentage of valid votes is: 100% - 3% = 97%

The total number of valid votes is: 2,40,000 × 97/100 = 2,32,800

The candidate received 60% of these valid votes. Therefore, the number of valid votes polled in favour of the candidate is: 2,32,800 × 60/100 = 1,39,680

Explanation

The mean proportion of two numbers a and b is given by the formula √(a × b).

Given the numbers 0.14 and 2.24, we substitute them into the formula:

Mean Proportion = √(0.14 × 2.24)

By converting the decimals into fractions:

Mean Proportion = √((14/100) × (224/100)) Mean Proportion = √((14 × 14 × 16) / 10000) Mean Proportion = √((14² × 4²) / 100²) Mean Proportion = (14 × 4) / 100 Mean Proportion = 56/100 = 0.56

Explanation

To find the percentage change, the formula is: Percentage Change = ((Final Value - Initial Value) / Initial Value) × 100

Substituting the given values: Initial Value = 4/5 Final Value = 5/6

The absolute change in the quantity is: 5/6 - 4/5 = (25 - 24) / 30 = 1/30

Now, calculate the percentage change: Percentage Change = ((1/30) / (4/5)) × 100 = (1/30 × 5/4) × 100 = 5/120 × 100 = 1/24 × 100 = 25/6% ≈ 4.17%

Explanation

Let the printed price of the article be ₹100.

The retailer gets a 40% discount, making the cost price for the retailer: CP = 100 - 40 = ₹60

The retailer sells the article at the printed price: SP = ₹100

Profit made by the retailer: Profit = SP - CP = 100 - 60 = ₹40

Profit percentage = (Profit / CP) × 100% Profit percentage = (40 / 60) × 100% = ⅔ × 100% = 200/3% = 66 ⅔%

Explanation

For a circle with radius R = 25 cm, a perpendicular drawn from the center O to a chord bisects the chord.

For the first chord of length 48 cm, the half-length is 24 cm. Using the Pythagorean theorem, the perpendicular distance OM from the center to this chord is: OM = √(25² - 24²) = √(625 - 576) = √49 = 7 cm

The distance between the two parallel chords is 27 cm. Since this distance is greater than OM, the second chord must lie on the opposite side of the center.

The perpendicular distance ON of the second chord from the center is: ON = 27 - OM = 27 - 7 = 20 cm

Using the Pythagorean theorem for the second chord with distance ON = 20 cm and radius R = 25 cm, the half-length of the second chord CN is: CN = √(25² - 20²) = √(625 - 400) = √225 = 15 cm

The total length of the second chord is: 2 × CN = 2 × 15 = 30 cm

Explanation

In the right-angled triangle BDC, the angle BDC is 90° because BD is perpendicular to AC. Since E is a point on BC, the angle EBD is the same as angle CBD, which is given as 40°.

In triangle BDC, the sum of angles is 180°: angle BCD = 180° - 90° - 40° = 50°

This means the angle ECA (or angle C) of triangle AEC is 50°.

Since E lies on the line segment BC, the angle BEA is an exterior angle of triangle AEC at vertex E. By the exterior angle theorem, the exterior angle of a triangle is equal to the sum of its two opposite interior angles: angle BEA = angle EAC + angle ECA x = 38 + 50 = 88

Explanation

The perpendicular distance d from the origin (0, 0) to a line of the form Ax + By + C = 0 is given by the formula:

d = |C| / √(A² + B²)

For the given line equation 6x + 8y - 48 = 0, the coefficients are A = 6, B = 8, and C = -48. Substituting these values into the formula:

d = |-48| / √(6² + 8²) d = 48 / √(36 + 64) d = 48 / √100 d = 48 / 10 d = 4.8 units

Explanation

Solving using BODMAS, first the bracket: 3 ÷ (1/3) = 9, so 9 - 3 = 6, and 2 × 6 = 12. Next, 27 ÷ 3 = 9, and 27 ÷ 9 + 3 = 3 + 3 = 6. Substituting these values gives [7 + 9 - 12 + 9 + 6 - 6] + 2 = 13 + 2 = 15.

Explanation

To find the difference between the total number of computers manufactured by Company A and Company C during the period from 2010 to 2014, we calculate the total production for each company.

Total computers manufactured by Company A: 240 + 300 + 1250 + 470 + 320 = 2580 thousand

Total computers manufactured by Company C: 270 + 490 + 430 + 1180 + 550 = 2920 thousand

The difference between the two totals: 2920 - 2580 = 340 thousand

Explanation

The arc length of a sector (L) with radius r and central angle θ is given by the formula:

L = (θ / 360°) × 2πr

Substituting the given values, θ = 120°, r = 7 cm, and π = 22/7:

L = (120 / 360) × 2 × (22/7) × 7

L = (1/3) × 2 × 22

L = 44/3 cm

Explanation

The average speed is calculated using the formula: Average Speed = Total Distance / Total Time

The distance covered in the first hour is: d₁ = 90 km/hr × 1 hr = 90 km

The distance covered in the next two hours is: d₂ = 120 km/hr × 2 hr = 240 km

Total distance covered is: Total Distance = 90 km + 240 km = 330 km

Total time taken is: Total Time = 1 hr + 2 hr = 3 hr

Substituting these values into the formula: Average Speed = 330 km / 3 hr = 110 km/hr

Explanation

The relationship between Simple Interest (SI), Principal (P), Rate (R), and Time (T) is given by the formula:

SI = (P × R × T) / 100

From the given ratio of principal to simple interest, let the principal P be 10 and the simple interest SI be 7. The time period T is 5 years.

Substituting these values into the formula:

7 = (10 × R × 5) / 100

7 = 50 × R / 100

7 = R / 2

R = 14%

Explanation

Correct Answer: B

The surface area of a cube with side length s is given by the formula A = 6s². When each side of the cube is tripled, the new side length becomes 3s.

The new surface area is: A_new = 6(3s)² = 54s²

The increase in the surface area is: 54s² - 6s² = 48s²

The percentage increase in the surface area is calculated by dividing the increase by the original surface area and multiplying by 100: (48s² / 6s²) × 100% = 8 × 100% = 800%

This can also be determined directly using scaling: scaling the linear dimensions of a shape by a factor of k scales its surface area by k². Tripling the sides (k = 3) scales the area by 3² = 9. This represents an increase of 9 - 1 = 8 times the original area, which corresponds to an 800% increase.

Explanation

To find which two banks disbursed the same sum of loan over all four years, calculate the total loan disbursed by each bank:

Total loan disbursed by Bank C = 20 + 25 + 15 + 20 = 80 crores

Total loan disbursed by Bank D = 15 + 20 + 35 + 10 = 80 crores

Both Bank C and Bank D have disbursed an equal sum of 80 crores over the four-year period.

Explanation

The volume of a sphere of radius r is given by the formula V = 4/3 πr³.

When three spheres of radii r₁, r₂, and r₃ are melted to form a single big sphere of radius R, the volume of the big sphere is equal to the sum of the volumes of the three smaller spheres:

4/3 πR³ = 4/3 πr₁³ + 4/3 πr₂³ + 4/3 πr₃³

Dividing both sides by 4/3 π gives:

R³ = r₁³ + r₂³ + r₃³

Substituting the given values r₁ = 75 cm, r₂ = 60 cm, and r₃ = 45 cm:

R³ = 75³ + 60³ + 45³

To simplify the calculation, factor out the greatest common divisor of 75, 60, and 45, which is 15:

R³ = (15 × 5)³ + (15 × 4)³ + (15 × 3)³ R³ = 15³ × (5³ + 4³ + 3³) R³ = 15³ × (125 + 64 + 27) R³ = 15³ × 216

Since 216 = 6³:

R³ = 15³ × 6³ R³ = (15 × 6)³ R³ = 90³

Taking the cube root of both sides gives:

R = 90 cm

Explanation

The fourth proportion d to three numbers a, b, and c is given by the formula d = (b × c) / a.

Substituting the given values a = 1.25, b = 5.75, and c = 3.5 into the formula:

d = (5.75 × 3.5) / 1.25

To simplify, first divide 5.75 by 1.25:

5.75 / 1.25 = 575 / 125 = 23 / 5 = 4.6

Now, multiply this result by 3.5:

d = 4.6 × 3.5 = 16.1

Explanation

The single equivalent discount for two successive discounts of x% and y% is given by the formula: Equivalent discount = x + y - (x × y)/100

Substituting x = 23 and y = 7: Equivalent discount = 23 + 7 - (23 × 7)/100 = 30 - 1.61 = 28.39%

The first discount is 37%. The difference between the two discount percentages is: 37% - 28.39% = 8.61%

The difference in money value on the amount of ₹2,635 is: 8.61% of 2,635 = (8.61 / 100) × 2,635 = 0.0861 × 2,635 = 226.8735

Rounding to two decimal places, the difference is 226.87.

Explanation

For any two similar triangles, the ratio of their areas is equal to the ratio of the squares of their corresponding sides. This relation is given by the formula:

Area₁ / Area₂ = (side₁ / side₂)²

Substituting the given values into the formula:

490 / 640 = (21 / side₂)²

Simplifying the fraction on the left side:

49 / 64 = (21 / side₂)²

Taking the square root on both sides:

7 / 8 = 21 / side₂

Solving for side₂:

side₂ = 21 × 8 / 7

side₂ = 24 cm

Explanation

The area of the playground leveled by the roller is equal to the curved surface area of the cylindrical roller multiplied by the total number of revolutions.

First, convert the dimensions of the roller from centimeters to meters: Diameter, d = 35 cm = 0.35 m Length (height), h = 100 cm = 1 m

The curved surface area (CSA) of a cylinder is given by the formula: CSA = π × d × h

Substituting the values: CSA = (22/7) × 0.35 × 1 = 22 × 0.05 = 1.1 m²

The total area leveled in 200 revolutions is: Total Area = CSA × Number of revolutions Total Area = 1.1 × 200 = 220 m²

Explanation

The total amount to be paid at the end of the investment period is calculated using the formula for simple interest and total amount.

Simple Interest (SI) = (P × R × T) / 100

Substituting the given values: Principal (P) = 4500 Rate of interest (R) = 8% per annum Time (T) = 4 years

SI = (4500 × 8 × 4) / 100 = 45 × 32 = 1440

The total amount (A) to be paid is the sum of the principal and the simple interest:

Amount (A) = Principal + SI Amount (A) = 4500 + 1440 = 5940

Explanation

The altitude of an equilateral triangle is given by the formula h = (√3/2) * a, where a is the side length. Substituting h = 3√3 cm gives the side length a = 6 cm, which yields an area of (1/2) * base * height = (1/2) * 6 * 3√3 = 9√3 square centimeters.

Explanation

By Pythagoras' theorem in right-angled triangle ABC: AB = √(AC² + BC²) AB = √(5² + 12²) = √169 = 13 cm

The area of triangle ABC can be calculated in two ways: Area = ½ × AC × BC = ½ × AB × CD

This simplifies to: CD = (AC × BC) / AB

Substituting the given values: CD = (5 × 12) / 13 = 60/13 = 4 8/13 cm

Explanation

The net profit percentage can be calculated using the successive multiplier method:

When the shopkeeper cheats 25% while buying, he gets 125 units of rice for the price of 100 units. This gives a weight multiplier of 125/100 = 5/4.

When he cheats 25% while selling, he delivers only 75 units of rice while charging the customer for 100 units. This gives a weight multiplier of 100/75 = 4/3.

He sells the rice at a nominal profit of 12½%, which is equal to 1/8. This gives a price multiplier of 1 + 1/8 = 9/8.

The net ratio of Selling Price to Cost Price is the product of these individual multipliers: Net Ratio = (5/4) × (4/3) × (9/8) = 15/8

Net Profit Percentage = (15/8 - 1) × 100% = (7/8) × 100% = 87.5%

Explanation

To find the time taken by X and Z together, we can determine their work rates. Taking the total work as 72 units, the combined rate of X, Y, and Z is 6 units/day, X and Y is 4 units/day, and Y and Z is 3 units/day. This gives individual rates of 3 units/day for X and 2 units/day for Z, meaning X and Z together work at 5 units/day and will complete the job in 72/5 days, which is 14 2/5 days.

Explanation

When a journey is divided into three equal parts travelled at speeds x, y, and z, the average speed of the entire journey is given by the formula:

Average Speed = 3 / (1/x + 1/y + 1/z)

Substituting the given values x = 80 km/h, y = 60 km/h, and z = 30 km/h:

Average Speed = 3 / (1/80 + 1/60 + 1/30)

Taking the least common multiple of the denominators 80, 60, and 30, which is 240:

1/80 + 1/60 + 1/30 = 3/240 + 4/240 + 8/240 = 15/240 = 1/16

Using this sum in the average speed formula:

Average Speed = 3 / (1/16) = 3 × 16 = 48 km/h