Three positive numbers are in the ratio of 4 : 5 : 7, and the sum of their squares is 15,210. Find the sum of the three numbers.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 3)

Answer 1

Given:

The ratio of the three positive numbers are 4 : 5 : 7

Sum of squares of the three numbers is 15,210

Concept Used:

Multiplying numerator and denominator with a value does not effect the ratio.

Calculation:

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

Then, their squares are \((4x)^2 = 16x^2\), \((5x)^2 = 25x^2\), and \((7x)^2 = 49x^2\), respectively.

According to the problem statement, the sum of their squares is 15,210.

Therefore, \(16x^2 + 25x^2 + 49x^2 = 15210 \)

Simplifying the equation, we get:

\(90x^2 = 15210 \)

Dividing both sides by 90, we get:

\(x^2 = 169 \)

Taking the square root of both sides, we get:

x = 13

Therefore, the three numbers are:

4x = 4 × 13 = 52,

5x = 5 × 13 = 65,

7x = 7 × 13 = 91

The sum of these three numbers is:

52 + 65 + 91 = 208

∴ The sum of the three numbers is 208.

Shortcut TrickLet the three numbers be 4x, 5x, and 7x,

Sum of these 3 numbers,

⇒ 4x + 5x + 7x = 16 x

Now considering the options there is only one option which is a multiple of 16

Hence option 4 is the correct answer.