Question

Find two numbers in the ratio 8:7 such that when each is decreased by 25/2, they are in the ratio 11:9.

Answer 1

Hope this helps u...

Answer 2

Answer:

40 and 35

Step-by-step explanation:

Given : two numbers in the ratio 8:7

To Find : Find two numbers in the ratio 8:7 such that when each is decreased by 25/2, they are in the ratio 11:9.

Solution:

Let the two numbers be a and b

So, $\frac{a}{b}=\frac{8}{7}$

$a=\frac{8}{7}b$  --1

Now  each is decreased by 25/2, they are in the ratio 11:9

So, $\frac{a-\frac{25}{2}}{b-\frac{25}{2}}=\frac{11}{9}$

$\frac{2a-25}{2b-25}=\frac{11}{9}$

$9(2a-25)=11(2b-25)$

$18a-225=22b-275$

$275-225=22b-18a$

Using 1

$50=22b-18(\frac{8}{7}b)$

$50=\frac{10b}{7}$

$350=10b$

$35=b$

Substitute in 1

$a=\frac{8}{7}(35)$

$a=40$

So, a = 40 and b = 35

Hence The two numbers are 40 and 35