Question

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the
-atio between the new numbers so formed is 5 : 7. Find the original number

Answer 1

Solution :-

Let the two numbers be x and y.

According to the first condition :-

$\longrightarrow \sf \dfrac{x}{y} = \dfrac{3}{5} \\\\ \longrightarrow x = \dfrac{3}{5}y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+10}{y+10}= \dfrac{5}{7}\\\\\longrightarrow 7(x+10) = 5(y+10) \\\\\longrightarrow 7x+70 = 5y+50 \\\\\longrightarrow 7x-5y = -20 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(2)$

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

$\longrightarrow \sf 7 \times \dfrac{3}{5}y - 5y = -20 \\\\\longrightarrow \dfrac{21y}{5}-5y = -20 \\\\\longrightarrow \dfrac{21y-25y}{5} = -20 \\\\\longrightarrow 21y-25y = -100\\\\\longrightarrow -4y = -100 \\\\\longrightarrow \bf y = 25$

Substitute y = 25 in eq(1) :-

$\longrightarrow \sf x = \dfrac{3}{5} \times 25 \\\\\longrightarrow x = 3 \times 5 \\\\\longrightarrow \bf x = 15$

The two numbers are 15 and 25.