Question

If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of
squares of the numbers is:
(a) 6:12:13
(b) 1: 2:4
(c) 36:144: 324
(d) None of these​

Answer 1

Answer=36:144:324

Let the nos. be =x,2x,3x

ATQ-

(x+2x+3x)/2=18

(6x)/2=18

3x=18

x=6

Therefore the numbers are=x=6,2x=12,3x=18

therefore 6^2:12^2:18^2

=36:144:324(ans)

Answer 2

The ratio of squares of the numbers is 36 : 144 : 324.

Three numbers are in the ratio of 1 : 2 : 3 and half the sum is 18.

We have to find the ratio of squares of the numbers.

Let proportionality constant is x.

then numbers are ; x , 2x and 3x

a/c to question,

half of the sum of numbers = 18

⇒half of the sum of these numbers = (x + 2x + 3x)/2 = 18

⇒6x/2 = 18

⇒3x = 18

⇒x = 6

now, numbers are ; 6 , 2 × 6 , 3 × 6 or, 6 , 12 , 18.

square of 6 = 6² = 36

square of 12 = 12² = 144

square of 18 = 18² = 324

∴ the ratio of squares of numbers = 36 : 144 : 324

Therefore the correct option is (c) 36 : 144 : 324.