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Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers

Solution:

Let us consider the two numbers to be x and y.

According to the first condition,

Ratio of these two numbers = 5 : 6

x : y = 5 : 6

x/y = 5/6

y = 6x/5----------------(1)

According to the second condition,

If, 8 is subtracted from each of the numbers, then ratio becomes 4 : 5

x - 8/y - 8 = 4/5

5x - 40 = 4y - 32

5x - 4y = 8-------------(2)

Substitute the value of y from (1) in (2),we get,

5x - 4(6x/5) = 8.

25x - 24x = 40

x = 40.

Substitute the value of x in (1),we get,

y = 6/5 x 40 = 6 x 8 = 48.

y = 48.

x = 40

y = 48.

Therefore, the required numbers are 40 and 48.

✦ Try This: Two numbers are in the ratio 4 : 5. If 8 is subtracted from each of the numbers, the ratio becomes 2 :3. Find the numbers

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 18

Summary:

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. The numbers are 40 and 48

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