1 .

Two years ago the ratio of the ages of Manoj and Shyam was 15 : 11. Two years hence the ratio of their ages will be 17 : 13. What is the present age of Shyam?

[ A ]    24 years
[ B ]    26 years
[ C ]    28 years
[ D ]    22 years
[ E ]    None of these
 Answer : Option A Explanation : Let the present age of Manoj and Shyam be x years and y years respectively. Then, two year ago, $x - 2 \over y - 2$ = $15 \over 11$ or, 11x - 22 = 15y - 30 or, 11x - 15y = -8 ... (i) Again, after two years, $x + 2 \over y + 2$ = $17 \over 13$ or, 13x + 26 = 17y + 34 or, 13x - 17y = 8 ... (ii) Multiplying eqn (i) by 13 and eqn (ii) by 11, we get 143x - 195y = - 104 - 143 + 187y = - 88 ---------------------------- y = 24 years
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