Question

The ratio of ages of two persons 10 years ago was 7:5. The average of their ages now is 40. The difference between their present age is: [Microfocus]

Answer 1

Solution:

⏭ Given:

✏ The ratio of ages of two persons 10 years ago was 7:5

✏ The average of their ages at present is 40

⏭ To Find:

✏The difference between their present age is...

⏭ Assumption:

✏ Let, present ages of person A and B are x and y respectively.

⏭ Calculation:

• Case-I

$\implies \sf \: \dfrac{x - 10}{y - 10} = \dfrac{7}{5} \\ \\ \implies \sf \: 5x - 50 = 7y - 70 \\ \\ \implies \sf \: \red{7y - 5x = 20} \: ..... \: (1)$

• Case-II

$\implies \sf \: \dfrac{x + y}{2} = 40 \\ \\ \implies \sf \: \blue{ x + y = 80} \: ..... \: (2)$

✏ By solving both equations, we get...

$\circ \sf \: \underline{present \: age \: of \: person \: A = 45 \: years} \\ \\ \circ \sf \: \underline{present \: age \: of \: person \: B = 35 \: years} \\ \\ \therefore \boxed{ \tt{ \pink{Difference \: between \: present \:ages = 10 \: years}}}$

Answer 2

Given-

• The ratio of ages of two persons 10 years ago is 7:5
• The average of their ages at present is 40

To Find-

• The difference between their present age is...

Calculation-

$\begin{lgathered}\implies \sf \: \dfrac{x - 10}{y - 10} = \dfrac{7}{5} \\ \\ \implies \sf \: 5x - 50 = 7y - 70 \\ \\ \implies \sf \: {7y - 5x = 20} \: ..... \: (1)\end{lgathered}$

$\begin{lgathered}\implies \sf \: \dfrac{x + y}{2} = 40 \\ \\ \implies \sf \: { x + y = 80} \: ..... \: (2)\end{lgathered}$

By comparing both equations, we get.....

Present age of person A = 45 years

Present age of person B = 35 years

Difference = (45-35) years

=> 10 years