Question

present age of A and B are in ratio 3:2 after 6 years, the ratio of their age is 11:8. find their present age?​

Answer 1

Answer:

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Present ages of A and B are 27 years and 18 years respectively.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Present age Ratio = 3 : 2

Ratio of Ages after 6 years = 11 : 8

To Find :

Their present Ages

Solution :

Consider the present Ages as :

• A as 3x
• B as 2x

★ $\boxed{\sf{ \frac{3x + 6}{2x + 6} = \frac{11}{8}}}$

$\sf{\implies} \:{\dfrac{3x + 6}{2x + 6} = \dfrac{11}{8}}$

$\sf{\implies} \: 8(3x + 6) = 11(2x + 6)$

$\sf{\implies} \: 24x + 48 = 22x + 66$

$\sf{\implies} \: 24x - 22x= 66 - 48$

$\sf{\implies} \: 2x= 18$

$\sf{\implies} \: x= \dfrac{18}{2}$

$\sf{\implies} \: x= 9$

$\rule{300}{1.5}$

★ Value of 3x

$\sf{\implies} \: 3 \times 9$

$\sf{\implies} \: 27$

A = 27 Years

★ Value of 2x

$\sf{\implies} \: 2 \times 9$

$\sf{\implies} \: 18$

B = 18 Years

$\therefore$ Present ages of A and B are 27 years and 18 years respectively.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Add 6 to the present ages, and check if the new ratio formed is 11 : 8

$\sf{\implies} \: \dfrac{27 + 6}{18 + 6}$

$\sf{\implies} \: \dfrac{33}{24}$

$\sf{\implies} \: \dfrac{33 \div 3}{24 \div 3} = \dfrac{11}{8}$

$\sf{\implies} \: 11 : 8$

$\therefore$ Present ages of A and B are 27 years and 18 years respectively.