Question

Two numbers are in ratio of 5:8. If 9 be added to each, the ratio becomes 8:11. Find both the numbers. ​

Answer 1

Answer:

Two numbers are in the ratio of 5:8 if 9 be added to each they are in the ratio of 8:11 find the numbers

Answer 2

Given:

The ratio of two numbers=5:8

New ratio=8:11

To find:

The two numbers

Solution:

The two numbers are 15 and 24.

We can find the numbers by following the given steps-

We know that the two numbers are in the ratio of 5:8.

So, let the two numbers be 5X and 8X.

Now, if 9 is added to both the numbers, the ratio becomes 8:11.

If 9 is added to 5X, we get 5X+9.

If 9 is added to 8X, we get 8X+9.

Taking the ratio of these two numbers, we get

(5X+9):(8X+9)=8:11

(5X+9)/(8X+9)=8/11

On cross multiplying,

(5X+9)×11=(8X+9)×8

55X+99=64X+72

99-72=64X-55X

27=9X

X=27/9

X=3

Now, the two numbers are 5X and 8X.

We will substitute the value of X to obtain the numbers.

5X=5×3=15

8X=8×3=24

Therefore, the two numbers are 15 and 24.