Question

two numbers are in ratio 7:11. If 7 is added to each of the numbers, the ratio becomes 2:3. Find the numbers. Please tell me i am stuck on this question

Answer 1

Answer:

49 and 77

Step-by-step explanation:

The numbers are in ratio 7:11

let the common multiple of the numbers be x

so the numbers will be 7x and 11x.

According to second condition,

ratio of 7x + 7 and 11x + 7 is 2:3

$\frac{7x + 7}{11x + 7} = \frac{2}{3}$

Solving the equation we get

$3(7x + 7) = 2(11x + 7)$

Solving further, we get

$x = 7$

Now, the original numbers were 7x and 11x

7x = 7 × 7 = 49

11x = 11 × 7 = 77

Verification:

$\frac{49}{77} = \frac{7}{11}$

$\frac{49 + 7}{77 + 7} = \frac{56}{84} = \frac{2}{3}$