RRB NTPC CBT 1 2020 Mathematics Questions with Solutions

Explanation

The Coefficient of Variation (C.V.) measures the relative variability of a dataset and is given by the formula:

C.V. = (Standard Deviation / Mean) × 100%

Substituting the given values:

C.V. = (5 / 40) × 100% = (1 / 8) × 100% = 12.5%

Explanation

When two items are sold at the same selling price, one at a gain of x% and the other at a loss of x%, there is always an overall net loss given by the formula:

Loss % = (x / 10)²

Substituting x = 10: Loss % = (10 / 10)² = 1² = 1%

Alternatively, calculating individual cost prices: Cost Price of first toy = 990 ÷ 1.10 = ₹900 Cost Price of second toy = 990 ÷ 0.90 = ₹1100 Total Cost Price = 900 + 1100 = ₹2000 Total Selling Price = 990 + 990 = ₹1980 Net Loss = 2000 - 1980 = ₹20 Loss % = (20 ÷ 2000) × 100 = 1%

Explanation

The length of the longest pole that can fit inside a rectangular room is equal to the length of the space diagonal of the cuboid.

Diagonal = √(l² + b² + h²)

Substituting l = 30 m, b = 15 m, and h = 10 m:

Diagonal = √(30² + 15² + 10²) = √(900 + 225 + 100) = √1225 = 35 m

Explanation

If the areas of three adjacent faces of a cuboid are a, b, and c, then a = lw, b = wh, and c = hl. Multiplying these gives abc = (lwh)² = V², which means the volume V = sqrt(abc) = (abc)^(1/2).

Explanation

Aligning the numbers by their decimal points and adding column by column:

6202.50000

• 620.25000
• 62.02500
• 6.20250
• 0.62025 ─────────────── 6891.59775

Summing the decimals from right to left gives .59775 in the fractional part, and summing the whole numbers with the carry gives 6891, yielding a total of 6891.59775.

Explanation

In compound interest, the interest earned during any year is calculated on the amount accumulated at the end of the preceding year.

Interest for the 3rd year = Amount after 3 years - Amount after 2 years = ₹1700 - ₹1600 = ₹100

Rate of interest R = (Interest for 3rd year / Amount after 2 years) × 100 R = (100 / 1600) × 100 = 100 / 16 = 6.25%

Explanation

Let the required number be x.

Since the difference between the number and its 25% is 24: x - 25% of x = 24 x - 0.25x = 24 0.75x = 24 ¾ x = 24 x = 24 × (4/3) = 32

Explanation

The prime numbers less than 55 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and 53. Counting these gives a total of 16 prime numbers.

Explanation

Using the algebraic identity, if a + b + c = 0, then a³ + b³ + c³ = 3abc.

Let a = x - y, b = y - z, and c = z - x.

Adding these three terms gives: a + b + c = (x - y) + (y - z) + (z - x) = 0

Since the sum of the three terms is zero, applying the identity directly gives: (x - y)³ + (y - z)³ + (z - x)³ = 3(x - y)(y - z)(z - x)

Explanation

Multiply both the numerator and denominator inside the square root by 10 to remove the decimal points:

√(36.1 / 102.4) = √(361 / 1024)

Taking the square root of the numerator and denominator individually gives:

√361 = 19 √1024 = 32

Therefore, √(361 / 1024) = 19 / 32.

Explanation

Total number of formal learners = 39 + 52 = 91 Total number of informal learners = 65 + 78 = 143 Total number of illiterates = 143 + 169 = 312

Ratio of Formal Learners : Informal Learners : Illiterates = 91 : 143 : 312

Dividing each value by their common factor of 13: 91 ÷ 13 = 7 143 ÷ 13 = 11 312 ÷ 13 = 24

The simplified ratio is 7 : 11 : 24.

Explanation

Total work = LCM(20, 30, 60) = 60 units.

Efficiency of Avinash = 60 / 20 = 3 units/day Efficiency of Bhuvnesh = 60 / 30 = 2 units/day Efficiency of Chaman = 60 / 60 = 1 unit/day

Work done in a 3-day cycle: Day 1: Avinash alone = 3 units Day 2: Avinash alone = 3 units Day 3: Avinash, Bhuvnesh, and Chaman together = 3 + 2 + 1 = 6 units

Total work completed in 3 days = 3 + 3 + 6 = 12 units.

Number of 3-day cycles required to complete 60 units = 60 / 12 = 5 cycles.

Total days taken = 5 × 3 = 15 days.

Explanation

The fraction of money remaining after each round is obtained by multiplying the retention factor of each round:

Fraction remaining = (1 - 1/3) × (1 - 3/5) × (1 - 4/7) = 2/3 × 2/5 × 3/7 = 4/35

Explanation

The ratio of copper, zinc, and lead in the mixture is 13 : 6 : 1.

Total parts = 13 + 6 + 1 = 20 parts

Given that zinc represents 6 parts of the total weight: Weight of 1 part = 90 ÷ 6 = 15 kg

Total weight of the machine part = 20 × 15 = 300 kg

Explanation

Let the two numbers be x and y (where x > y).

Using the standard formulas for two numbers given their sum (S) and difference (D): x = (S + D) / 2 = (20 + 2.5) / 2 = 11.25 y = (S - D) / 2 = (20 - 2.5) / 2 = 8.75

The required ratio of the two numbers is: x : y = 11.25 : 8.75 = 1125 : 875 = 9 : 7

Explanation

Convert the given mixed fractions into improper fractions: Total flour available = 9 ¼ = 37/4 kg Flour required per loaf = 1 ⅛ = 9/8 kg

Number of loaves = Total flour ÷ Flour per loaf = (37/4) ÷ (9/8) = (37/4) × (8/9) = 74/9 = 8.22...

Rounding 8.22... to the nearest whole number yields 8.