Question

The numbers are in the ratio 2:3.if 4 be subtracted from each, they are in the ratio 3:5. The numbers are​

Answer 1

Step-by-step explanation:

let no. 2x and 3x

(2x-4/(3x-4)=3/5

10x-20=9x-12

x=8

numbers are 2×8=16 and3×8=24

Answer 2

Given:

• 2 numbers are in the ratio 2:3
• 4 is subtracted from each number.
• The new ratio becomes 3:5

To find:

1. The 2 numbers are ?

Method:

Let the 2 numbers be 2x and 3x.

$\sf{\dfrac{2x-4}{3x-4}= \dfrac{3}{5}}\\\\\\\\\rm{On \: Cross \: Multiplication}\\\\\implies \sf{5 (2x - 4) = 3(3x - 4)}\\\\\\\implies \sf{10x - 20 = 9x - 12}\\\\\\\implies \sf{10x - 9x = 20 - 12}\\\\\\\implies \boxed{\bf{x=8}}$

We know that 2 numbers are 2x and 3x

2x = 2 × 8 = 16

3x = 3 × 8 = 24

Therefore the 2 numbers are 16 and 24

Verification:

Let us substitute the 2 numbers in the given criteria of the question

$\sf{ \dfrac{16}{24}= \dfrac{2}{3}}$

$\sf{Now, \: if \: 4 \: is \: subtracted,}\\\\\sf{ \dfrac{16 - 4}{24 - 4} = \dfrac{12}{20} = \dfrac{3}{5}}$

★Hence verified ★