Question

Two numbers are in ratio of 3 :4of 10 is added to each number the ratio becomes 5 : 6 then find the number .

Answer 1

${\underline{\sf{Question}}}$

Two numbers are in ratio of 3 :4.If 10 is added to each number the ratio becomes 5 : 6 then find the number .

${\underline{\sf{Solution}}}$

Let the numbers be 3x and 4x.

According to the question

If 10 is added to each number the ratio becomes 5 : 6.

$\sf \implies \dfrac{3x + 10}{4x + 10} = \dfrac{5}{6}$

$\sf \implies6(3x + 10) = 5(4x + 10)$

$\sf \implies20x - 18x = 60 - 50$

$\sf \implies 2x = 10$

$\sf \implies \: x = 5$

Therefore ,

One number = 3x = 15

and other number = 4x = 20

$\rule{200}2$${\underline{\sf{Verification}}}$

If 10 is added to each number the ratio becomes 5 : 6

$\sf \dfrac{ 15+ 10}{20 + 10} = \dfrac{5}{6}$

Hence , Verified

Answer 2

Given :

• Two numbers are in ratio of 3:4.
• If 10 is added to each number ,the ratio becomes 5:6.

To find :

• Two numbers.

Solution :

Consider,

• 1st number = 3x
• 2nd number = 4x

According to the question :-

• If 10 is added to each number ,the ratio becomes 5:6.

$\implies\sf{(3x+10)\::\:(4x+10)=5\::\:6}$

$\implies\sf{\dfrac{3x+10}{4x+10}=\dfrac{5}{6}}$

$\implies\sf{20x+50=18x+60}$

$\implies\sf{20x-18x=60-50}$

$\implies\sf{2x=10}$

$\implies\sf{x=5}$

Therefore,

• 1st number = 3×5 = 15
• 2nd number = 4×5 = 20

Hence , the two numbers are 15 and 20.

_____________________

Verification :-

• 1st number = 15
• 2nd number = 20

Ratio of two numbers = 3:4

→ 15 : 20 = 3 : 4

→ 3 : 4 = 3 : 4

After adding 10 with each number ,

• 1st number = (15+10)=25
• 2nd number = (20+10) = 30

Ratio of two numbers = 5:6

→ 25 : 30 = 5 : 6

→ 5 : 6 = 5 : 6

Hence Verified __!!

_____________________