Question

Two numbers A and B are in the ratio 2 : 5. If 6 is added to each of them, then the
ratio becomes 5:8. If 2 is subtracted from each of them, then the ratio becomes
1:4. Find the sum of squares of those numbers.
a) 116
b) 125
c) 256
d) 289​

Answer 1

Answer:

Option a) 116 .

Step-by-step explanation:

We are given that Two numbers A and B are in the ratio 2 : 5 which means let Numerator, A = 2$x$   and   Denominator, B = 5$x$

• First condition says that if 6 is added to each of them, then the

        ratio becomes 5:8 i.e;

                         ⇒  $\frac{2x+6}{5x+6}=\frac{5}{8}$

                         ⇒ 8(2$x$ + 6) = 5(5$x$ + 6)

                         ⇒  16$x$ + 48 = 25$x$ + 30

                         ⇒  25$x$ - 16$x$ = 48 - 30   ⇒  $9x$ = 18

So, from here we get $x$ = 2 .

• Second condition says that if 2 is subtracted from each of them, then the  ratio becomes 1:4 i.e;

                          ⇒ $\frac{2x-2}{5x-2}=\frac{1}{4}$

                          ⇒ 4(2$x$ - 2) = 5$x$ - 2

                          ⇒ 8$x$ - 5$x$ = -2 + 8   ⇒ 3$x$ = 6

From here also we get $x$ = 2 .

So, the Two numbers are A = 2$x$ = 2 * 2 = 4   and  B = 5$x$ = 5 * 2 = 10.

Hence, sum of squares of two numbers = $4^{2} + 10^{2}$ = 16 + 100 = 116 .

Therefore, option a) is correct.

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