Question

The ratio of two numbers is 2:3.If both the numbers are increased by 8their ratio becomes 10:13.Find the numbers.

Answer 1

Let the ratio be x

then the two numbers will be 2x and 3x

according to the question...

$\frac{2x+8}{3x +8}=\frac{10}{13}\\13(2x+8)=10(3x+8)\\26x+104= 30x+80\\4x=24\\x=6\\\\therefore\\2x = 12\\3x=18$

Answer 2

Answer:

• The numbers are 12 and 18 respectively.

Step-by-step explanation:

Given that:

• The ratio of two numbers is 2 : 3.
• Id both the numbers are increased by 8, their ratio becomes 10 : 13.

To Find:

• The numbers.

Let us assume:

• The numbers be 2x and 3x respectively.

After adding 8 to both the numbers:

• 1st number = 2x + 8
• 2nd number = 3x + 8

According to the question,

$\sf{\implies2x+8:3x+8=10:13}$

Writing the ratios in fraction,

$\sf{\implies\dfrac{2x+8}{3x+8}=\dfrac{10}{13}}$

By cross-multiplication,

$\sf{\implies13(2x+8)=10(3x+8)}$

Opening the brackets,

$\sf{\implies26x+104=30x+80}$

Transposing variables to LHS, constants to RHS and changing their sign,

$\sf{\implies26x-30x=80-104}$

Subtracting,

$\sf{\implies-4x=-24}$

$\sf{\implies\not\!{-}4x=\not\!{-}24}$

$\sf{\implies4x=24}$

Transposing 4 from LHS to RHS and changing its sign,

$\sf{\implies x=\dfrac{24}{4}}$

Dividing the numbers,

$\bf{\implies x=6}$

Hence,

• x = 6

Therefore,

• 1st number = 2x = 2 × 6 = 12

• 2nd number = 3x = 3 × 6 = 18