Question
The sum of two positive integers multiplied by the bigger number is 204, and their difference multiplied by the smaller number is 35. The numbers are:
Answer: Option A
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Let the numbers be `x` and y such that `x` > y. Then
`x(x + y)` = 204 `rArr` `x^2 + xy` = 204...............(i) and y(`x` - y) = 35 `rArr` ` xy - y^2` = 35 ............(ii)
Subtracting (ii) from (i), we get : `x^2 + y^2` = 169
The only triplet satisfying this condition is (12, 5, 13) Thus , `x` = 12, y= 5.
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