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### Question

The sum of two numbers is 53. Their difference is 15. They are in the ratio?

**A**

$1{15/19}$.

**B**

$2{17/18}$.

**C**

${5/7}$.

**D**

$4{1/3}$.

**Soln.**

**Ans: a**

Let the numbers be a and b, and let their ratio be k such that $a/b = k$. We are given $a + b = 53$ ⇒ $b(k + 1) = 53$. Similarly, from the difference we can obtain $b(k - 1) = 15$. Dividing we get ${k + 1}/{k - 1} = 53/15$. By componendo and dividendo, $k = {53 + 15}/{53 - 15}$ = ${34/19}$, which is same as: $1{15/19}$.