SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

Total runs scored in the first 36 overs = 36 × 4.3 = 154.8 runs

Remaining runs required to reach the target of 271 runs = 271 - 154.8 = 116.2 runs

Required run rate in the remaining 14 overs = 116.2 ÷ 14 = 8.3 runs/over

Explanation

The total profit of Rs. 187200 is to be divided among Amit, Brijmohan, and Chiranjeev in the ratio 1:2:5.

The sum of the ratio terms is 1 + 2 + 5 = 8 parts.

Chiranjeev's share represents 5 parts out of these 8 parts. The calculation is: (5 / 8) × 187200 = 5 × 23400 = 117000

Explanation

Let the speed of the Express train be E km/hr and the speed of the Rajdhani train be R km/hr.

According to the first condition, the Express train takes 6 hours more than Rajdhani to travel 732 km: 732/E - 732/R = 6 122/E - 122/R = 1

According to the second condition, when the speed of the Express train is doubled, it takes 3 hours less than Rajdhani: 732/R - 732/(2E) = 3 732/R - 366/E = 3 244/R - 122/E = 1

Adding these two equations to eliminate the variable E: (122/E - 122/R) + (244/R - 122/E) = 1 + 1 122/R = 2 R = 61 km/hr

Explanation

A rhombus is a quadrilateral with all four sides equal. When a diagonal is drawn in a rhombus, it divides the shape into two congruent isosceles triangles. For instance, in a rhombus ABCD with diagonal AC, the triangles ABC and ADC are congruent because all four sides of the rhombus are equal (AB = AD and BC = DC) and they share the side AC. Corresponding parts of congruent triangles are equal, which means angle BAC equals angle DAC, and angle BCA equals angle DCA. This proves that the diagonal AC bisects the opposite angles A and C. The same property applies to the other diagonal BD, which bisects opposite angles B and D. Therefore, the diagonals of a rhombus always bisect its opposite angles.

Explanation

Using the trigonometric identity sin(-θ) = -sin(θ), we can write: sin(-240°) = -sin(240°)

Since 240° lies in the third quadrant, it can be written as 180° + 60°. Using the identity sin(180° + θ) = -sin(θ): sin(240°) = sin(180° + 60°) = -sin(60°)

Substituting this value back into the first equation: sin(-240°) = -(-sin(60°)) = sin(60°)

The standard value of sin(60°) is √3/2. Therefore, the value of x is √3/2.

Explanation

To simplify the fraction 3774/2958, find the Highest Common Factor (HCF) of the numerator and the denominator using the Euclidean division algorithm:

3774 = 2958 × 1 + 816 2958 = 816 × 3 + 510 816 = 510 × 1 + 306 510 = 306 × 1 + 204 306 = 204 × 1 + 102 204 = 102 × 2 + 0

The HCF of 3774 and 2958 is 102. Dividing both the numerator and the denominator by 102 gives:

3774 ÷ 102 = 37 2958 ÷ 102 = 29

This simplifies the fraction to 37/29.

Explanation

The effective discount in a buy-x-get-y-free offer is calculated using the standard percentage relation:

Discount % = (Number of free items / Total number of items received) × 100

In this promotion, the customer receives a total of 4 shirts (3 paid + 1 free) while only paying for 3. The discount is the value of the 1 free shirt out of the total 4 shirts.

Substituting these values:

Discount % = (1 / 4) × 100 = 25%

Since the price of each shirt is identical at Rs 500, the ratio of the free shirt value to the total marked price of all 4 shirts remains exactly 1/4, resulting in an effective discount of 25% per shirt.

Explanation

Using the fundamental trigonometric identity: 1 + tan²A = sec²A

Taking the square root on both sides: √(1 + tan²A) = secA

Given that x = √(1 + tan²A), we directly get: x = secA

Explanation

We can simplify the expression in Option C by taking a common denominator for the two terms:

cosecA/(cosecA - 1) + cosecA/(cosecA + 1)

Combining the fractions over the common denominator (cosecA - 1)(cosecA + 1) gives:

[cosecA(cosecA + 1) + cosecA(cosecA - 1)] / [(cosecA - 1)(cosecA + 1)]

Expanding the numerator and the denominator, we get:

(cosec²A + cosecA + cosec²A - cosecA) / (cosec²A - 1)

= 2cosec²A / (cosec²A - 1)

Using the standard trigonometric identity cosec²A - 1 = cot²A, the expression becomes:

2cosec²A / cot²A

Since cosecA = 1/sinA and cotA = cosA/sinA, we can express this in terms of sine and cosine:

[2 × (1/sin²A)] / (cos²A/sin²A)

Simplifying the fraction by canceling sin²A in the denominators:

2 / cos²A

Since 1/cos²A = sec²A, this simplifies to:

2sec²A

Explanation

The total value of each category of stock is found by multiplying its quantity by its average cost.

Value of Mobile Phones stock = 30 × 11,000 = 3,30,000 rupees Value of Cameras stock = 54 × 12,000 = 6,48,000 rupees Value of TVs stock = 65 × 58,000 = 37,70,000 rupees Value of Refrigerators stock = 61 × 22,000 = 13,42,000 rupees Value of ACs stock = 65 × 26,000 = 16,90,000 rupees

Summing these individual values gives the total stock value: Total Value = 3,30,000 + 6,48,000 + 37,70,000 + 13,42,000 + 16,90,000 = 77,80,000 rupees

Since 1 lakh equals 1,00,000, we convert this total value into lakh rupees by dividing by 1,00,000: Total Value in lakh rupees = 77,80,000 / 1,00,000 = 77.8 lakh rupees.

Explanation

In 2012, the Import/Export ratio is 0.7. Since imports are ₹1100 crores, the exports for 2012 are calculated as: Exports in 2012 = 1100 / 0.7 = 11000/7 ≈ 1571.43 crores

The combined exports for 2012 and 2013 are ₹6000 crores, so the exports for 2013 are: Exports in 2013 = 6000 - 11000/7 = 31000/7 ≈ 4428.57 crores

In 2013, the Import/Export ratio is 1.2. Thus, the imports for 2013 are: Imports in 2013 = 1.2 × Exports in 2013 Imports in 2013 = 1.2 × 31000/7 = 37200/7 ≈ 5314.29 crores

Explanation

To find the increase in the height of the child from the 6th Birthday to the 15th Birthday, we subtract the height on the 6th Birthday from the height on the 15th Birthday.

From the given data table: Height of the child on the 15th Birthday = 180 cms Height of the child on the 6th Birthday = 115 cms

The calculation for the increase in height is: 180 cms - 115 cms = 65 cms

Explanation

The total duration from 10 pm to 6 am is 8 hours.

The values given in the data table represent percentages because they sum up to 100 (10 + 15 + 5 + 5 + 65 = 100).

The combined percentage of time spent Dreaming or Awake is: 15% + 65% = 80%

To find the duration of time spent in these two states, calculate 80% of the total 8 hours: 8 hours × 80% = 6.4 hours

Explanation

The expansion of a product of two binomials of the form (x + a)(x + b) is given by the formula x² + (a + b)x + ab.

Substituting a = 4 and b = -2 into the formula: (x + 4)(x - 2) = x² + (4 + (-2))x + (4 × -2) (x + 4)(x - 2) = x² + 2x - 8

Explanation

The relationship between two numbers, their Highest Common Factor (HCF), and their Lowest Common Multiple (LCM) is given by the formula:

Product of two numbers = HCF × LCM

Substituting the given values into the formula:

88 × 33 = 11 × LCM

LCM = (88 × 33) ÷ 11

LCM = 8 × 33

LCM = 264

Explanation

To divide 299a²b² by 23b², we can express the division as a fraction:

(299a²b²) / (23b²)

This can be solved by dividing the numerical coefficients and the algebraic variables separately:

(299 / 23) × (a²b² / b²)

Dividing the numerical part: 299 ÷ 23 = 13

Dividing the algebraic part: The term b² in the numerator and the denominator cancels out, leaving only a²: a²b² / b² = a²

Multiplying the simplified components yields: 13 × a² = 13a²

Explanation

Solving the first inequality: x + 3 ≤ 2x + 4 Subtracting x and 4 from both sides gives: -1 ≤ x

Solving the second inequality: 4 - x ≥ 3x - 2 Adding x and 2 to both sides gives: 6 ≥ 4x x ≤ 6/4 x ≤ 1.5

Combining both conditions gives the range for x: -1 ≤ x ≤ 1.5

Among the options, only x = 1 lies within this interval.

Explanation

The number of terms divisible by 7 between 150 and 300 can be found by identifying the multiples of 7 in this range.

The first multiple of 7 greater than 150 is 154 (which is 7 × 22). The last multiple of 7 less than 300 is 294 (which is 7 × 42).

These terms form an arithmetic progression where: First term (a) = 154 Last term (l) = 294 Common difference (d) = 7

Using the formula for the n-th term of an arithmetic progression: l = a + (n - 1)d

Substituting the values: 294 = 154 + (n - 1) × 7 140 = (n - 1) × 7 20 = n - 1 n = 21

Alternatively, this can be calculated using the floor division function: Number of multiples of 7 up to 300 = floor(300 / 7) = 42 Number of multiples of 7 up to 150 = floor(150 / 7) = 21 Total multiples between 150 and 300 = 42 - 21 = 21

Explanation

Let the speed of the goods train be v km/hr.

The goods train passes the station 2 hours before the second train. Therefore, when the second train passes the station, the goods train has already covered a distance of: Distance = Speed × Time = 2v km

Since both trains are traveling in the same direction, the relative speed of the second train with respect to the goods train is: Relative Speed = 63 - v km/hr

The second train overtakes the goods train in 7 hours by covering the initial gap of 2v km. Using the formula Distance = Relative Speed × Time: 2v = (63 - v) × 7 2v = 441 - 7v 9v = 441 v = 49 km/hr

Explanation

The ratio of the efficiency of Abhi to Bhishma is 4:1. Since the time taken to complete a work is inversely proportional to efficiency, the ratio of the time taken by Abhi and Bhishma is 1:4.

Let the time taken by Abhi be x days and by Bhishma be 4x days.

The difference in time taken is: 4x - x = 90 3x = 90 x = 30

Thus, Abhi takes 30 days and Bhishma takes 120 days to complete the work individually.

Using the combined work formula, the time taken by both working together is: (30 × 120) / (30 + 120) = 3600 / 150 = 24 days

Explanation

Using the simple interest formula, Interest = (P × R × T) / 100, where P is the principal, R is the rate of interest per annum, and T is the time period in years. Let the common rate of interest be R.

For the loan to Jaafar: Interest₁ = (10600 × R × 4) / 100 = 424R

For the loan to Kailas: Interest₂ = (7300 × R × 3) / 100 = 219R

The sum of both interests is: 424R + 219R = 643R

Setting this equal to the total interest of Rs 2250.5: 643R = 2250.5 R = 2250.5 / 643 = 3.5%

Explanation

The bus fare is increased in the ratio 5:7, which means the ratio of the original fare to the new fare is 5:7.

Let the original fare be 5x and the new fare be 7x.

Given that the original fare is Rs 625: 5x = 625 x = 125

The increase in the fare is the difference between the new fare and the original fare: Increase = 7x - 5x = 2x

Substituting the value of x: Increase = 2 × 125 = Rs 250

Explanation

The total revenue for 11 years is calculated by multiplying the number of years by the average revenue: 11 × 66 = 726 lakhs

The sum of the revenues for the first 6 years is: 6 × 61 = 366 lakhs

The sum of the revenues for the last 6 years is: 6 × 73 = 438 lakhs

Since the sixth year is included in both the first 6 years and the last 6 years, the revenue of the sixth year is the difference between the combined sum of these two periods and the total revenue of the 11 years: Revenue of the sixth year = (366 + 438) - 726 = 804 - 726 = 78 lakhs

Explanation

The intercept form of the equation of a line with x-intercept a and y-intercept b is:

x/a + y/b = 1

Given that the x-intercept a = 5/3 and the y-intercept b = -4/5, we substitute these values into the formula:

x / (5/3) + y / (-4/5) = 1

Simplifying the fractions:

3x/5 - 5y/4 = 1

To clear the denominators, multiply the entire equation by 20, which is the least common multiple of 5 and 4:

20 × (3x/5) - 20 × (5y/4) = 20 × 1

12x - 25y = 20

Explanation

Euler's formula for any convex polyhedron states that V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. An octahedron by definition has 8 faces, meaning F = 8. Given that the number of edges E = 12, we substitute these values into the formula to find the number of vertices:

V - 12 + 8 = 2 V - 4 = 2 V = 6

This direct calculation yields exactly 6 vertices for the octahedron.

Explanation

The effective discount percentage can be directly calculated using the formula:

Discount % = (Number of free items / Total number of items) × 100

In this offer, on purchasing 1 t-shirt, 2 t-shirts are received free. This means the customer gets a total of 3 t-shirts (1 purchased + 2 free) while paying the price of only 1.

Discount % = (2 / 3) × 100 = 66.67%

Explanation

Circumference of a circle is given by the formula C = 2πr. Using r = 10.5 cm (which is 21/2 cm) and π = 22/7, the circumference is:

C = 2 × (22/7) × (21/2) = 66 cm

The perimeter of an equilateral triangle with side length a is P = 3a. Since the circumference of the circle is equal to the perimeter of the triangle:

3a = 66 a = 22 cm

Explanation

The curved surface area of a right circular cone is given by the formula: Curved Surface Area = πrl

Given that the curved surface area is 3080 sq cm and the radius r is 28 cm, we can find the slant height l: 3080 = (22/7) × 28 × l 3080 = 88 × l l = 3080 / 88 l = 35 cm

The relation between slant height l, radius r, and height h of a cone is: l² = r² + h² 35² = 28² + h² 1225 = 784 + h² h² = 1225 - 784 h² = 441 h = √441 = 21 cm

The volume V of a cone is given by the formula: V = (1/3) × π × r² × h V = (1/3) × (22/7) × 28 × 28 × 21 V = 22 × 28 × 28 V = 17248 cubic cm

Explanation

The secant function is the reciprocal of the cosine function, defined as sec θ = 1/cos θ.

To evaluate sec 7π/4, the angle 7π/4 can be rewritten using its reference angle in the fourth quadrant: 7π/4 = 2π - π/4

Using the trigonometric identity cos(2π - θ) = cos θ: cos 7π/4 = cos(2π - π/4) = cos π/4

Since the value of cos π/4 is 1/√2: cos 7π/4 = 1/√2

Taking the reciprocal to find the secant value: sec 7π/4 = 1 / (1/√2) = √2

Explanation

Let the total income of the man be ₹100.

The expenditure is 68% of his income, which is ₹68.

The savings will be the remaining portion of his income: 100 - 68 = ₹32

To find the percentage of his expenditure that he saves, we use the relation: Percentage = (Savings / Expenditure) × 100

Substituting the values into the formula: Percentage = (32 / 68) × 100 = (8 / 17) × 100 = 800 / 17 ≈ 47.06%

Explanation

Expanding the terms using the standard trigonometric sum and difference identities:

sin(A + B) = sinA cosB + cosA sinB

sin(A - B) = sinA cosB - cosA sinB

Adding these two equations:

sin(A + B) + sin(A - B) = (sinA cosB + cosA sinB) + (sinA cosB - cosA sinB)

The positive and negative cosA sinB terms cancel each other out:

sin(A + B) + sin(A - B) = 2 sinA cosB

Explanation

Using the algebraic identity (a - b)(a + b) = a² - b², the expression expands to: (secA - cosA)(secA + cosA) = sec²A - cos²A

We can rewrite sec²A and cos²A using standard trigonometric identities: sec²A = 1 + tan²A cos²A = 1 - sin²A

Substituting these identities into the expanded equation gives: sec²A - cos²A = (1 + tan²A) - (1 - sin²A) = 1 + tan²A - 1 + sin²A = tan²A + sin²A

Explanation

Let the volume of pure milk purchased be 3 litres. Cost Price (CP) of 3 litres of milk at Rs 20 per litre = 3 × 20 = Rs 60.

The milkman adds 1/3 of water to it, which is 1/3 × 3 = 1 litre of water. Total volume of the resulting mixture = 3 + 1 = 4 litres.

Selling Price (SP) of 4 litres of mixture at Rs 25 per litre = 4 × 25 = Rs 100.

Total Gain = SP - CP = 100 - 60 = Rs 40.

Gain percentage = (Total Gain / CP) × 100 Substituting the values: Gain percentage = (40 / 60) × 100 = 66.67%

Explanation

Total number of employees = 3 + 12 + 4 = 19

Total bonus for Managers = 3 × (30,00,000 × 60%) = 3 × 18,00,000 = 54,00,000

Total bonus for Executives = 12 × (12,00,000 × 30%) = 12 × 3,60,000 = 43,20,000

Total bonus for Trainees = 4 × (4,00,000 × 10%) = 4 × 40,000 = 1,60,000

Total bonus paid to all employees = 54,00,000 + 43,20,000 + 1,60,000 = 98,80,000

Average bonus per employee = Total bonus ÷ Total number of employees = 98,80,000 ÷ 19 = 5,20,000

Explanation

To find the pair of years with equal total exports, calculate the sum of exports for all three companies for the years 2013 and 2014.

Total exports in 2013 = 3000 + 2000 + 2000 = 7000 lakh rupees.

Total exports in 2014 = 2000 + 1000 + 4000 = 7000 lakh rupees.

Since the total exports for both 2013 and 2014 are equal to 7000 lakh rupees, this pair of years meets the requirement.

Explanation

The total profit or loss of the company over the last five years is calculated by taking the sum of the profit or loss values for each year from 2011 to 2015:

Total = 10 + 15 + (-25) + (-5) + 20

Total = 25 - 25 - 5 + 20

Total = 15

Since the resulting sum is positive, the company made a profit of Rs 15 crores.

Explanation

To find the percentage share of Jewellery in total exports, first calculate the total value of all exports in 2015:

Total exports = Jewellery + Software + Cotton + Steel + Electronics Total exports = 1000 + 700 + 700 + 875 + 875 = 4150 million USNow, calculate the percentage of Jewellery exports:

Percentage share of Jewellery = (Value of Jewellery / Total exports) × 100 Percentage share of Jewellery = (1000 / 4150) × 100 Percentage share of Jewellery = 100000 / 4150 ≈ 24.1%

Explanation

The given polynomial is 4x³ - 2x² + 2x - 3. In this expression, the term containing x² is -2x². The numerical factor multiplying x² is -2, which represents its coefficient.

Explanation

Let the list price of the article be L and the cost price be C.

In the first case, a discount of 40% is offered on the list price, meaning the selling price is 60% of L. This sale results in a 10% loss, which means the selling price is also equal to 90% of the cost price C.

0.6L = 0.9C L = 1.5C

In the second case, a discount of 20% is offered on the list price, so the new selling price is 80% of L. Substituting the relationship between L and C:

New Selling Price = 0.8L = 0.8 × 1.5C = 1.2C

Since the selling price is 1.2 times the cost price, the merchant makes a profit. The profit percentage is calculated as:

Profit % = (1.2C - C)/C × 100% = 0.2 × 100% = 20%

Explanation

The formula for the combined mean of three groups is (n₁x̄₁ + n₂x̄₂ + n₃x̄₃) / (n₁ + n₂ + n₃), where n₁, n₂, n₃ represent the number of students in each division and x̄₁, x̄₂, x̄₃ represent their respective mean marks.

Using the given data: n₁ = 60, x̄₁ = 66 n₂ = 45, x̄₂ = 62 n₃ = 75, x̄₃ = 60

The ratio of the number of students in divisions A, B, and C is 60 : 45 : 75. Dividing by the greatest common divisor of 15 simplifies the weights to 4 : 3 : 5.

Substituting these simplified weights into the weighted mean formula: Combined Mean = (4 × 66 + 3 × 62 + 5 × 60) / (4 + 3 + 5) = (264 + 186 + 300) / 12 = 750 / 12 = 62.5

Explanation

To divide 221a²b² by 13b², we perform the division of the coefficients and the algebraic variables separately:

(221a²b²) ÷ (13b²) = (221 ÷ 13) × a² × (b² ÷ b²)

Dividing the numerical coefficients, 221 ÷ 13 = 17. Dividing the variable parts, b² ÷ b² = 1, leaving the a² term unchanged.

Combining these results gives 17a².

Explanation

To find the value of x, simplify the given equation:

40.36 - (9.347 - x) - 29.02 = 3.68

First, remove the parentheses:

40.36 - 9.347 + x - 29.02 = 3.68

Combine the positive and negative constant terms on the left side:

(40.36 - 29.02) - 9.347 + x = 3.68

11.34 - 9.347 + x = 3.68

1.993 + x = 3.68

Now, isolate x by subtracting 1.993 from both sides:

x = 3.68 - 1.993

x = 1.687

Explanation

Solving the first inequality: x + 3 ≤ 4x + 4 3x ≥ -1 x ≥ -1/3

Solving the second inequality: 5(4 - x) - 4 ≥ 5x - 2 20 - 5x - 4 ≥ 5x - 2 16 - 5x ≥ 5x - 2 10x ≤ 18 x ≤ 1.8

Combining the two inequalities gives the range of x as: -1/3 ≤ x ≤ 1.8

The value x = 1 lies within this interval, making it the valid solution that satisfies both inequalities.

Explanation

To convert speed from kilometres per hour (km/h) to metres per second (m/s), use the standard conversion factor of 5/18.

Speed in m/s = Speed in km/h × 5/18

Substituting the given value of 1116 km/h into the formula:

Speed = 1116 × 5/18

First, divide 1116 by 18:

1116 ÷ 18 = 62

Now, multiply by 5:

62 × 5 = 310 m/s

This means the missile travels a distance of 310 metres in one second.

Explanation

The area of a circle is directly proportional to the square of its radius, represented as A = πr². When the radius r increases by a percentage, the net percentage change in the area can be calculated using the successive percentage change formula:

Net percentage increase = x + y + xy/100

Since the radius increases by 31% in both dimensions of the area formula, we substitute x = 31 and y = 31:

Net percentage increase = 31 + 31 + (31 × 31)/100 Net percentage increase = 62 + 961/100 Net percentage increase = 62 + 9.61 Net percentage increase = 71.61%

Explanation

The first deposit of Rs 6000 is made on 1st January. Since it remains in the bank for the entire year, it compounds for 2 half-years at a rate of 20% per half-year.

The accumulated amount from the first deposit at the end of the year is: A₁ = 6000 × (1 + 0.20)² = 6000 × (1.2)² = 6000 × 1.44 = Rs 8640

The second deposit of Rs 6000 is made on 1st July. It compounds for only 1 half-year (from 1st July to 31st December) at the same rate of 20% per half-year.

The accumulated amount from the second deposit at the end of the year is: A₂ = 6000 × (1 + 0.20)¹ = 6000 × 1.2 = Rs 7200

The total amount accumulated at the end of the year is: Total Amount = A₁ + A₂ = 8640 + 7200 = Rs 15840

The total principal deposited by the customer during the year is: Total Principal = 6000 + 6000 = Rs 12000

The total interest gained by the customer is: Interest = Total Amount - Total Principal = 15840 - 12000 = Rs 3840

Explanation

If x is the third proportional of two numbers a and b, then the numbers are in continued proportion: a : b = b : x

This relation yields the formula: x = b² / a

Substituting the given values, a = 4 and b = 28: x = 28² / 4 x = (28 × 28) / 4 x = 7 × 28 x = 196

Explanation

Rate of baking by Mummy = 75 cakes ÷ 15 hours = 5 cakes per hour.

Combined rate of baking by Mummy and Sister together = 120 cakes ÷ 20 hours = 6 cakes per hour.

Rate of baking by Sister = Combined rate − Mummy's rate = 6 − 5 = 1 cake per hour.

Number of cakes Sister can bake in 30 hours = Sister's rate × 30 hours = 1 × 30 = 30 cakes.

Explanation

The numbers between 200 and 400 that are divisible by 7 form an arithmetic progression.

The first term after 200 divisible by 7 is 203. The last term before 400 divisible by 7 is 399.

In this arithmetic progression, the first term a is 203, the last term l is 399, and the common difference d is 7.

Using the formula for the number of terms n: n = (l - a)/d + 1

Substituting the values: n = (399 - 203)/7 + 1 n = 196/7 + 1 n = 28 + 1 n = 29

Alternatively, this can be calculated by finding the total multiples of 7 up to 399 and subtracting the multiples of 7 up to 200: Multiples of 7 up to 399 = floor(399/7) = 57 Multiples of 7 up to 200 = floor(200/7) = 28 Total multiples in the given range = 57 - 28 = 29

Explanation

When a point P(a,b) is reflected in the origin, its coordinates change sign, so the coordinates of P₁ are (-a,-b).

When the point P₁(-a,-b) is reflected in the y-axis, its x-coordinate changes sign while its y-coordinate remains the same, giving the point (a,-b).

We are given that this final reflected point is (6,-5). Therefore: (a,-b) = (6,-5)

Comparing the coordinates gives: a = 6 -b = -5, which means b = 5

Thus, the coordinates of point P are (6,5).