Question

two numbers are in the ratio 7 is to 11 if 7 is added to each of the number the ratio becomes 2 is to 3 find the numbers

Answer 1

Solution:-

Let the two number be x and y.

$= > \frac{x}{y} = \frac{7}{11} \\ \\ = > 11x = 7y \\ \\ = > x = \frac{7}{11} y$

After adding 7 to the numbers. we get,

$= > \frac{x + 7}{y + 7} = \frac{2}{3} \\ \\ = 3(x + 7) = 2(y + 7) \\ \\ = > 3x + 21 = 2y + 14 \\ \\ = > 3x - 2y + 21 - 14 = 0 \\ \\ = > 3x - 2y + 7 = 0$
Putting x = 7y/11 here, we get

$= > 3 \times \frac{7y}{11} - 2y = - 7 \\ = > \frac{21y}{11} - 2y = - 7 \\ \\ = > \frac{21y - 22y}{11} = - 7 \\ \\ = > - y = - 77 \\ \\ = > y = 77$


Putting y=77 in equation 1. we get,

$= > x = \frac{7y}{11} \\ \\ = > x = \frac{7 \times77 }{11} \\ \\ = > x = 7 \times 7 \\ \\ = > x = 49$

Hence,

The two numbers are 49 and 77.

Answer 2

Answer:49,77

Step-by-step explanation: