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### Question

The sum of two numbers is 25. Their difference is 19. They are in the ratio?

**A**

$7{1/3}$.

**B**

$12{1/2}$.

**C**

$6{1/3}$.

**D**

$6{1/5}$.

**Soln.**

**Ans: a**

Let the numbers be a and b, and let their ratio be k such that $a/b = k$. We are given $a + b = 25$ ⇒ $b(k + 1) = 25$. Similarly, from the difference we can obtain $b(k - 1) = 19$. Dividing we get ${k + 1}/{k - 1} = 25/19$. By componendo and dividendo, $k = {25 + 19}/{25 - 19}$ = ${22/3}$, which is same as: $7{1/3}$.