Question

b. Two numbers are in the ratio 4: 5. If 4 is added to each term, the ratio becomes 25: 31. Find the original numbers.
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Answer 1

Answer:

Given:

Two numbers are in the ratio 4 : 5.

Let the numbers be 4x , 5x.

And also given that,

If 4 is added to each , the ratio becomes 25 : 31.

According to the question,

$\frac{4x + 4}{5x + 4} = \frac{25}{31}$

After cross multiplication we get,

$31(4x + 4) = 25(5x + 4) \\ \\ 124x + 124 = 125x + 100 \\ \\ 124x - 125x = 100 - 124 \\ \\ - x = - 24 \\ \\ x = 24.$

Hence, the numbers are 4x = 96 & 5x = 120

Answer 2

Two numbers are in the ratio 4:5.

Let us assume that the first number is 4M and the second number be 5M.

If 4 is added to each term, the ratio becomes 25:31.

After adding 4..

• First number = 4M + 4
• Second number = 5M + 4

$\small{\sf{\:\:\:\:\:\:\:\:\:{\underline{As\:per\:given\:condition}}}}$

$\implies\:\sf{\dfrac{4M+4}{5M+4}\:=\:\dfrac{25}{31}}$

Cross-multiply them

$\implies\:\sf{31(4M+4)\:=\:25(5M+4)}$

$\implies\:\sf{124M+124\:=\:125M+100}$

$\implies\:\sf{124M-125M\:=\:100-124}$

$\implies\:\sf{-M\:=\:-24}$

$\implies\:\sf{M\:=\:24}$

Therefore,

First number = 4M = 4(24) = 96

Second number = 5M = 5(24) = 120