Question

There are 12 people in a book club. The ratio of men to women is 1:2. Two more men joined the club. What is the new ratio of men to women? Give your answer to simplest form

Answer 1

★ How to do :-

Here, we are given with the total number of people in a book club. We are also given with the ratio of men to women in the same club. We re asked to find the new ratio of men to women if two more men join the club. First, we should find the number of men and women who were there in the club before the joining of two mens. Then, we add the number of joined mens to original number of mens and then find the ratio value. So, let's solve!!

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➤ Solution :-

${\tt \leadsto 1 : 2 = 12}$

Insert a variable on both part of ratio.

${\tt \leadsto 1x + 2x = 12}$

Add the values on LHS.

${\tt \leadsto 3x = 12}$

Shift the number 3 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{12}{3}}$

Simplify the fraction on RHS.

${\tt \leadsto x = 4}$

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Number of men :-

${\tt \leadsto 1x = 1 \times 4}$

${\tt \leadsto Men = 4}$

Number of women :-

${\tt \leadsto 2x = 2 \times 4}$

${\tt \leadsto Women = 8}$

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New number of men :-

${\tt \leadsto 4 + 2 = 6}$

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New ratio :-

${\sf \leadsto Men : Women}$

Substitute the given values.

${\tt \leadsto 6 : 8}$

Write it as fraction and write in simplest form.

${\tt \leadsto \cancel \dfrac{6}{8} = \dfrac{3}{4}}$

Convert it back into ratio.

${\bf \leadsto \red{\underline{\boxed{\bf So, \: New \: ratio = 3 : 4}}}}$

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Hence solved !!