Numerical Ability Test - 4

Given:

The ratio of two weights = 27 kg = 27 × 1000 = 27000 g and 108 g

Calculation:

Required ratio = 27000 : 108

⇒ 250 : 1

∴ Required ratio is 250 : 1

Given:

a ∶ b = 3 ∶ 5

b ∶ c = 2 ∶ 3 

Calculation:

⇒ a ∶ b ∶ c = 6 ∶ 10 ∶ 15

∴ The value of a ∶ b ∶ c is 6 ∶ 10 ∶ 15

The correct option is 3 i.e. 6 ∶ 10 ∶ 15

Given:

Ratio of three numbers is 3 ∶ 2 ∶ 5

Sum of the squares of the three numbers is 1862

Calculation:

Let the three number be 3x ∶ 2x ∶ 5x

Sum of the squares of the three numbers = 9x² + 4x² + 25x² = 1862

38x² = 1862

x² = 49 or x = 7

Now, the middle number is 2x

The middle number will be 2x = 2 × 7 = 14

Given:

Men ∶ Women = 12 ∶ 11

Total population = 4,60,000

Calculation:

Men ∶ Women = 12 ∶ 11

Sum of ratios = 12 + 11 = 23

Population of women = 4,60,000 × \(\frac{11}{23}\)

Population of women = 2,20,000

The population of women is 2,20,000

Given:

Ratio of two numbers = 19 : 11

Difference between the numbers = 40

Calculation:

Let the numbers be 19x and 11x respectively

Then, according to the question,

19x - 11x = 40

⇒ 8x = 40

⇒ x = 5

⇒ Numbers are 95 and 55

∴ Sum of the numbers = 95 + 55 = 150

Given:

Three numbers are in the ratio 1/2 : 2/3 : 3/4. 

Largest number - Smallest number = 21

Calculation:

Given ratio = 1/2 : 2/3 : 3/4

⇒ 12 × 1/2 : 12 × 2/3 : 12 × 3/4

⇒ 6 : 8 : 9

Now, let the ratio be x 

1st Number = 6x, 2nd Number = 8x & 3rd Number = 9x 

Now, Again according to the question

9x - 6x = 21

⇒ 3x = 21

⇒ x = 7

Now, Sum of three numbers = 6x + 8x + 9x

⇒ Sum of three numbers = 23x

⇒ Sum of three numbers = 23 × 7 = 161

∴ The sum of three numbers is 161.

Let Tarun, Raghav and Kapil initially received Rs. ‘7x’, Rs. ‘4x’ and Rs. ‘9x’ respectively

But, Kapil gave 1/3 of his share each to Tarun and Raghav,

Hence,

Tarun’s final share = 7x + 9x/3 = 7x + 3x = 10x

Raghav’s final share = 4x + 9x/3 = 4x + 3x = 7x

Kapil’s final share = 9x/3 = 3x

Now, Tarun received Rs. 1800 more than Raghav,

⇒ 10x – 7x = 1800

⇒ 3x = 1800

⇒ x = 1800/3 = Rs. 600

Given:

Total number of coins of 20 paise and 25 paise = 324 

Total number coins makes Rs.71

Calculation:

Let the number of 25 paise coins = y 

⇒ No of 20 paise coins = 324 - y 

As per the question; 

y × 25/100 + (324 - y) × 20/100 = Rs.71

⇒ y/4 + (324 - y)× 1/5 = 71

⇒ y/4 + 324/5 - y/5 = 71 

⇒ y/20 = 71 - 324/5 

⇒ y/20 = 31/5

⇒ y = 124

∴ The number of 25 paise coins = 124 

Alternate Method By Alligation Method

Let all the 324 coins are of 20 paise coins; then amount = 324 × 20/100 

⇒ Rs.64.8

Let all the 324 coins are of 25 paise coins; then amount = 324 × 25/100 

⇒ 81 

But, in real the amount is Rs.71 

⇒ Ratio of 20 p coins & 25 p coins = 50 : 31

⇒ 50 + 31 = 81 

⇒ 81 = 324 coins 

⇒ 31 = 324/81 × 31 = 124

∴ The no 25 p coins = 124

Calculation:

Let the numbers are 7x and 9x

According to the question,

(7x+44)/(9x+44) = 11/13

⇒ 91x + 44 × 13 = 99x + 44 × 11

⇒ -8x = 44 × 11- 44 × 13 =

⇒ -8x = 44(11-13) 

⇒ -8x = -88

⇒ x = 11.

Now, Numbers = 7x = 7 × 11 = 77 and 9x = 9 x 11 = 99

Difference = 99 - 77 = 22

∴ The difference between the numbers is 22.

Given:

Three numbers are in ratio of 4 : 5 : 6

Sum of the numbers = 225

Calculation:

Let the numbers be 4x, 5x, and 6x respectively,

According to the question,

4x + 5x + 6x = 225

⇒ 15x = 225

⇒ x = 15

The middle number = 5x = 5 × 15 = 75

∴ The middle number is 75.