Question

two numbers are such that the ratio between them is 3 is to 5 if it is increased by 10 the ratio between the number 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),

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

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.

Answer 2

Answer:

the 2 numbers are 15 and 25