Question

The ratio between the ages of a and b at present is 2:3 five years hence the ratio of their ages will be 3:4 what is the present age of a

Answer 1

Let the present ages of A and B be x and y respectively.

According to first condⁿ

$\frac{x}{y} = \frac{2}{3} \\ x = \frac{2}{3} y \\ y = \frac{3x}{2}$

(always try to get denominators in factors of 2, 5 or 10)

Answer 2

• Let present age of a be "2M" years and present age of b be "3M" years.

Five years hence,

• Age of a = 2M + 5

• Age of b = 3M + 5

》 Five years hence, ratio of their ages becomes 3:4.

According to question,

$\rightarrow \: \dfrac{2M \: + \: 5}{3M \: + \: 5} \: = \: \dfrac{3}{4}$

Cross multiply them

$\rightarrow \: 4(2M \: + \: 5) \: = \: 3(3M \: + \: 5)$

$\rightarrow \: 8M \: + \: 20\: = \: 9M \: + \: 15$

$\rightarrow \: 8M \: - \: 9M\: = \: 15 \: - \: 20$

$\rightarrow \: - \: M\: = \: - \: 5$

$\rightarrow\boxed{ \: M\: = \: 5}$

So,

Present age of a = $2(5)$

$\rightarrow{10}$ years

Present age of b = $3(5)$

$\rightarrow{15}$ years

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Present age of a = 10 years.

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☆ VERIFICATION :

From above calculations we have M = 5

Put value of M in this :

$\dfrac{2M \: + \: 5}{3M \: + \: 5} \: = \: \dfrac{3}{4}$

=> $\dfrac{2(5) \: + \: 5}{3(5) \: + \: 5} \: = \: \dfrac{3}{4}$

=> $\dfrac{10 \: + \: 5}{15 \: + \: 5} \: = \: \dfrac{3}{4}$

=> $\dfrac{15}{20} \: = \: \dfrac{3}{4}$

=> $\dfrac{3}{4} \: = \: \dfrac{3}{4}$

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