Question

three numbers A,B,C are in the ratio 1/2:2/3:3/4 and their sums is 276 . Find the numbers​

Answer 1

★ How to do :-

Here, we are given with a ratio of three numbers A, B and C. They need to divide some money between them in some ratio. We are asked to find out how much amount does each of them get. So, first we should take a same variable x to all the part of ratios and then add them all. Then, we should transport the numbers from one hand side to other and then, we can find the value of x and then multiply with each part of ratio to get the answer. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{1}{2} : \dfrac{2}{3} : \dfrac{3}{4} = 276}$

Insert a variable x for all the parts of ratio.

${\tt \leadsto \dfrac{1}{2}x + \dfrac{2}{3}x + \dfrac{3}{4}x = 276}$

Convert the fractions into like fractions.

LCM of 2, 5 and 4 is 12.

${\tt \leadsto \dfrac{6}{12}x + \dfrac{8}{12}x + \dfrac{9}{12}x = 276}$

Add all the fractions that are having a variable x.

${\tt \leadsto \dfrac{23}{12}x = 276}$

Shift the fraction of LHS to RHS, changing it's sign.

${\tt \leadsto x = 276 \div \dfrac{23}{12}}$

Take the reciprocal of second fraction and multiply both the fractions.

${\tt \leadsto x = \dfrac{276}{1} \times \dfrac{12}{23}}$

Multiply the fractions.

${\tt \leadsto x = \dfrac{276 \times 12}{1 \times 23} = \dfrac{3312}{23}}$

${\tt \leadsto x = \cancel \dfrac{3312}{23} = \underline{144}}$

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Now, multiply the value of x with each part of the ratio.

Number obtained to 'A' :-

${\tt \leadsto \dfrac{1}{2}x = \dfrac{1}{2} \times 144}$

${\tt \leadsto \dfrac{144}{2} = \pink{\underline{\boxed{\tt 72}}}}$

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Number obtained to 'B' :-

${\tt \leadsto \dfrac{2}{3}x = \dfrac{2}{3} \times 144}$

${\tt \leadsto \dfrac{288}{3} = \pink{\underline{\boxed{\tt 96}}}}$

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Number obtained to 'C' :-

${\tt \leadsto \dfrac{3}{4}x = \dfrac{3}{4} \times 144}$

${\tt \leadsto \dfrac{432}{4} = \pink{\underline{\boxed{\tt 108}}}}$

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Hence solved !!