Question

Two numbers ate in the ratio 7:11. If 7 is affed to each of 5he numbers, the ratio becomes 2:3. Find the numbers.

Answer 1

Solution :-

Let the two numbers be x and y.

According to the first condition :-

$\longrightarrow \sf \dfrac{x}{y} = \dfrac{7}{11} \\\\\longrightarrow x = \dfrac{7}{11} y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+7}{y+7} = \dfrac{2}{3} \\\\\longrightarrow 3(x+7) = 2(y+7) \\\\\longrightarrow 3x+21 = 2y+14 \\\\\longrightarrow 3x-2y = -7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

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

$\longrightarrow \sf 3 \times \dfrac{7}{11} y - 2y = -7 \\\\\longrightarrow \dfrac{21y}{11} - 2y = -7 \\\\\longrightarrow \dfrac{21y-22y} {11} = -7 \\\\\longrightarrow -y = -77 \\\\\longrightarrow \bf y = 77$

Substitute y = 77 in eq (1) :-

$\longrightarrow \sf x = \dfrac{7}{11} \times 77 \\\\\longrightarrow x = 7 \times 7 \\\\\longrightarrow \bf x = 49$

The two number are 49 and 77.