SONU,MONU AND NANCY ARE RESIDENTS OF CERTAIN LOCALITY. NANCY IS 11 YEARS OLDER THAN MONU AND SONU IS THRICE AS OLD AS MONU. FIVE YEARS LATER,THE SUM OF AGES OF MONU AND SONU WILL BE TWO LESS THAN TWICE THE AGE OF NANCY. WHAT ARE THE RESPECTIVE PRESENT AGE OF NANCY AND SONU?

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Solution

Dear Student,

$L e t S o n u, M o n u a n d N a n c y' s a g e b e x, y a n d z y e a r s r e s p e c t i v e l y . A c c o r d i n g t o t h e q u e s t i o n : z = y + 11 x = 3 y A f t e r 5 y e a r s : x + 5 + y + 5 = 2 (z + 5) - 2 x + y + 10 = 2 z + 10 - 2 x + y + 10 = 2 z + 8 S u b s t i t u t i n g z = y + 11 a n d x = 3 y i n t h i s e q u a t i o n : 3 y + y + 10 = 2 (y + 11) - 2 4 y + 10 = 2 y + 22 - 2 4 y - 2 y = 22 - 2 - 10 2 y = 22 - 12 2 y = 10 y = \frac{10}{2} y = 5 y e a r s x = 3 y = 2 (5) = 15 y e a r s z = y + 11 = 5 + 11 = 16 y e a r s S o, N a n c y' s p r e s e n t a g e = z = 16 y e a r s S o n u' s p r e s e n t a g e = x = 15 y e a r s$

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