Ratio and Proportion Practice Question of 14 November 2022

Question of The Day14-11-2022

The ratio of three numbers is 4 : 5 : 7 and the sum of their cubes is 4256. Find the ratio of the sum of squares of 1^st two numbers to the sum of squares of last two numbers.

Answer

Correct Answer : a ) 41 : 74

Explanation :

According to the question:

Ratio of three numbers = 4 : 5 : 7

Let the numbers be 4x, 5x and 7x

(4x)³ + (5x)³+ (7x)³ = 4256

64x³ + 125x³ + 343x³ = 4256

532x³ = 4256

x³ = 4256/ 532

x³ = 8

x = 2

Thus, the numbers are

1^st number = 4x = 4 *2 = 8

2^nd number = 5x = 5 *2 = 10

3^rd number = 7x = 7 * 2 = 14

Therefore, sum of square of 1^st two numbers = (8)² + (10)² = 64 + 100 = 164

Sum of square of last two numbers = (10)² + (14)² = 100 + 196 = 296

Required ratio = 164 : 296

Required ratio = 41 : 74

Hence, (a) is the correct answer.

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