Question

Two numbers are in ratio of 3:4. If the 2 is subtract from the first no. and 5 is subtract from the second no. The ratio becomes reciprocal of the original ratio. Find the number.

Answer 1

Given:

• Two numbers are in ratio: 3:4

• If 2 is subtracted from first number and 5is subtracted from second number the ratio becomes reciprocal of 3:4

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Need to find:

• The numbers =?

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Solution:

Reciprocal of 3:4 = 4:3

Let the numbers be

• 3x and
• 4x.

After subtracting 2 from 1st number we get:

• 3x- 2

After subtracting 5 from 2nd number we get:

• 4x-5

Ratio of the new numbers will be:

$= \dfrac{3x - 2}{4x - 5}$

Also Given the ratio would be 4:3

Equating them we get,

$\dfrac{3x - 2}{4x - 5} = \dfrac{4}{3}$ (cross multiply)

$\implies \: 9x - 6 = 16x - 20$

$\implies \: 16x - 9x = 20 - 6$

$\implies \: 7x = 14$

$\implies \: x = 2$

The numbers are:

• 3x = 3×2= 6
• 4x= 4× 2 = 8

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Thus the numbers are 6 and 8