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 1st 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

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

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

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

Therefore, sum of square of 1st 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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