Question

5. The product of two numbers is 96 and their difference is 10. What is the sum of the two numbers? ଦୁଇଟି ସଂଖ୍ୟାର ଗୁଣଫଳ ୨% ଓ ସେମାନଙ୍କର ଅନ୍ତରଫଳ 10 ଅଟେ । ତେବେ ସଂଖ୍ୟା ଦୁଇଟିର ଯାଗଫଳ କେତେ ? (A) 16 B) 22 (C) 32 (D) 36
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Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The product of two numbers is 96 and their difference is 10. The sum of the two numbers

(A) 16

(B) 22

(C) 32

(D) 36

EVALUATION

Let the numbers are x and y

Since product of two numbers is 96

∴ xy = 96 - - - - - - - (1)

Now their difference is 10

∴ x - y = 10 - - - - - - (2)

Now we have

$\sf{ {(x + y)}^{2} = {(x - y)}^{2} + 4xy}$

$\sf{ \implies {(x + y)}^{2} = {(10)}^{2} + (4 \times 96)}$

$\sf{ \implies {(x + y)}^{2} = 100 +384}$

$\sf{ \implies {(x + y)}^{2} = 484}$

$\sf{ \implies {(x + y)}^{2} = {22}^{2} }$

$\sf{ \implies {(x + y)}^{} = 22}$

So the sum of numbers = 22

FINAL ANSWER

Hence the correct option is (B) 22

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