Question

two numbers are in the ratio 2:3. if 10 is added to each, they are in the ratio 4:5. find the two numbers?​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Two numbers are in ratio 2:3.

• If 10 is added to each number , ratio becomes 4:5.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• The two numbers .

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Let the two numbers be 'x' and 'y'.

So,

$\\ \sf \: \frac{x}{y} = \frac{2}{3} \\ \\ \\ \sf \: x = \frac{2y}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .....(1)$

Now , 10 is added to both the numbers , ratio becomes 4:5

$\\ \sf \: \frac{x + 10}{y + 10} = \frac{4}{5} \\ \\ \\ \sf \: 5(x + 10) = 4(y + 10) \\ \\ \\ \sf \: 5x + 50 = 4y + 40 \\ \\ \\ \sf \: 5x - 4y = 40 - 50 \\ \\ \\ \sf \: 5x - 4y = - 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .....(2)$

Putting eqⁿ (1) in eqⁿ (2) ,

We get...

$\\ \sf \: 5( \frac{2y}{3} ) - 4y = - 10 \\ \\ \\ \sf \: \frac{10y}{3} - 4y = - 10 \\ \\ \\ \sf \: \frac{10y - 12y}{3} = - 10 \\ \\ \\ \sf \: \frac{ - 2y}{3} = - 10 \\ \\ \\ \sf \: - 2y = - 30 \\ \\ \\ \boxed{\sf \: \green{y = 15}}$

Putting y = 15 in eqⁿ (2)

We get ,

$\\ \sf \: 5x - 4(15) = - 10 \\ \\ \\ \sf \: 5x - 60 = - 10 \\ \\ \\ \sf \: 5x = 50 \\ \\ \\ \boxed{ \sf \: \green{x = 10 }}$

Hence , numbers are 10 and 15.

Answer 2

The two numbers are 10 and 15

Given:

Two numbers are in the ratio 2:3

If 10 is added to each their ratio = 4:5  

To find:

The two numbers

Solution:

Let 2x and 3x are be the given numbers

After adding 10 to the number

The given numbers will  2x+10 and 3x+10

Given that after adding their ratio = 4 : 5

⇒ 2x+10 : 3x+10 = 4 : 5

⇒ $\frac{2x+10}{3x+10} = \frac{4}{5}$

⇒ 5(2x+10) = 4(3x+10)

⇒ 10x + 50 = 12x + 40

⇒ 2x = 10

⇒  x = 5

Therefore, the two number are

2x = 2(5) = 10

3x = 3(5) = 15

The two numbers are 10 and 15

#SPJ2