Question

The ratio of reema and seema is 7:3 after 6 years ratio is 5:3 . difference between their ages?

Answer 1

Let the ratio of their age be X years

Then their age = 7X years and 5X years

According to the question 7X+6/3X+6 = 5/3

(7X+6)3 = (3X+6)5

=> 21X + 18 = 15X +30

=> 6X = 12

=> X =2

Hence difference b/t their age = 4 years

Answer 2

Solution :-

Let :-

Present age of Reema = x

Present age of Seema = y

After 6 years :-

Age of Reema = x + 6

Age of Seema = y + 6

According to the first condition :-

$\longrightarrow \sf \dfrac{x}{y} = \dfrac{7}{3} \\\\\longrightarrow x = \dfrac{7}{3}y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...........................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+6}{y+6}= \dfrac{5}{3} \\\\\longrightarrow 3(x+6) = 5(y+6) \\\\\longrightarrow 3x+18 = 5y+30 \\\\\longrightarrow 3x-5y = 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Substitute the value of x in eq (2) :-

$\longrightarrow \sf 3 \times \dfrac{7}{3}y -5y = 12 \\\\\longrightarrow \dfrac{21y}{3}-5y = 12 \\\\\longrightarrow \dfrac{21y-15y}{3} = 12 \\\\\longrightarrow 6y = 36 \\\\\longrightarrow \bf y = 6$

Substitute y = 6 in eq (1) :-

$\longrightarrow \sf x = \dfrac{7}{3} \times 6 \\\\\longrightarrow x= 7 \times2 \\\\\longrightarrow \bf x = 14$

Present age of Reema = 14 years

Present age of Seema = 6 years

Difference between their ages = 14 - 6 = 8