Question

Two numbers are such that the ratio between them is 5 : 3. If each is increased by 10, the ratio between them becomes 7 : 5. What is the sum of the two numbers?

Answer 1

Hey friend,

Here is the solution for this question :-

Two numbers are in a ratio of 5:3 =

$\frac{5}{3}$

So, let the first number be 5k and the second number be 3k,

Now each increases by 10 ➡ 5k + 10 & 3k + 10

Now, the new ratio is 7:5

➡

$\frac{5k + 10}{3k + 10} = \frac{7}{5} \\ \\ now \: by \: cross \: multiplication \\ \\ 5(5k + 10) = 7(3k + 10) \\ \\ 25k + 50 = 21k + 70 \\ \\ 25k - 21k = 70 - 50 \\ \\ 4k = 20 \\ \\ k = \frac{20}{4} \\ \\ k = 5 \\ \\ now \: the \: first \: number \: = 5k = 5 \times 5 = 25 \\ \\ \\ second \: number = 3k = 3 \times 5 = 15$

So, the sum of the numbers =

$first \: number + second \: number \\ \\ 25 + 15 = 40$

Hence, the sum of the numbers is 40.

I hope this will help you....