Question

Two numbers are in the ratio 3:11. If 1 is added to the denominator the ration is
4:15. Find the number​

Answer 1

Answer

12 and 44

$\rule{100}2$

Explanation

Given,

ratio of two numbers is 3 : 11

Let, the first number be x and second be y

Then, x/y = 3/11

→ x = 3y/11

Also, when 1 is added to denominator, the ratio becomes 4 : 15

→ x/(y + 1) = 4/15

→ x = (4y + 4)/15

Equating the two values of x,

3y/11 = (4y + 4)/15

→ 45y = 44y + 44 (on cross multiplying)

→ y = 44

Then, x = 3y/11,

→ x = 3 × 44/11

→ x = 12

Therefore, the numbers are 12 and 44.

Answer 2

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

The numbers are 12 and 44

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

Let ,

The first number and second number be x and y

By the given condition ,

$\star \: \: \sf \frac{x}{y} = \frac{3}{11} \\ \\ \implies \sf</p><p>x = \frac{3y}{11} \: - - - \: eq (i)$

If 1 is added to denominator the ratio of numbers become 4 : 15 i.e

$\star \: \: \sf \frac{x}{y + 1} = \frac{4}{15} \: - - - eq(ii)$

Put the value of x = 3y/11 in equation (ii) , we get

$\implies \sf \frac{3y}{11 (y + 1) } = \frac{4}{15} \\ \\ \implies \sf \frac{45y}{11y + 11} = 4\\ \\ \implies \sf 45y = 4(11y + 11) \\ \\ \implies \sf 45y = 44y + 44 \\ \\ \implies \sf y = 44$

Now , put the value of y = 44 in eq (i) , we get

$\sf \implies x = \frac{3 \times \cancel{44}}{ \cancel{11}} \\ \\ \sf \implies x = 3 \times 4 \\ \\ \sf \implies x = 12$

Thus , the required numbers are 12 and 44