Question

Two numbers are in the ratio of 5: 6. If 7 is subtracted from each of the numbers, the ratio becomes 4: 5. Find the numbers.

Answer 1

Let the two numbers be x and y.
We have been given the ratio of two numbers 5:6

`"x"/"y"=5/6` ........(1)

when 7 is subtracted from each number the ratio becomes 4:5

`("x"-7)/("y"-7) = 4/5`............(2)

6x = 5y

⇒ 6x - 5y = 0 .............(3)

5 (x - 7) = 4(y - 7)

⇒ 5x - 35 = 4y - 28

⇒ 5x - 4y = 7 ..........(4)

Solving (3) and (4) by elimination method
Multiply (3) by 5 and (4) by 6

30 x - 25y = 0 ....................(5)

30 x - 24y = 42 ................(6)

Subtracting (5) from (6)

y = 42

Substitute y = 42 in (3) we get 

6x - 5 (42) = 0

⇒ 6x = 210

⇒ x = 35

Therefore, the two numbers are 35 and 42.