Three numbers $ A, B, C $ are in the ratio $ \frac{1}{2}: \frac{2}{3}: \frac{3}{4} $ and their sum is 276. Find the numbers.

Given:

A, B and C are in the ratio $\frac{1}{2} \ :\ \frac{2}{3} \ :\ \frac{3}{4}$  and  Sum of A, B and C is 276.

To find:

We have to find the value of A, B, and C.

Solution:

Let the common factor be = a

So,

$A\ =\ \frac{a}{2}$

$B\ =\ \frac{2a}{3}$

$C\ =\ \frac{3a}{4}$

Now,

$Sum\ of\ A,\ B\ and\ C\ =\ 276$

$\frac{a}{2} \ +\ \frac{2a}{3} \ +\ \frac{3a}{4} \ =\ 276$

$\frac{6a\ +\ 8a\ +\ 9a}{12} \ =\ 276$

$\frac{23a}{12} \ =\ 276$

$a\ =\ 276\ \times \ \frac{12}{23}$

$a\ =\ 12\ \times \ 12$

$\mathbf{a\ =\ 144}$

Therefore,

$A\ =\ \frac{a}{2} \ =\ \frac{144}{2} \ =\ \mathbf{72}$

$B\ =\ \frac{2a}{3} \ =\ \frac{288}{3} \ =\ \mathbf{96}$

$C\ =\ \frac{3a}{4} \ =\ \frac{432}{4} \ =\ \mathbf{108}$.

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Updated on: 10-Oct-2022

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