Question

Sum of the present ages of anu and binu is 65.after five years anu's age will be four times binus age. What are their ages now?​

Answer 1

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let age or anu is x

and binu is y

according to question;

$x + y = 65 \: ..........(i)$

after 5 years

age of anu = x+5

age of binu = y+5

according to question

x+5 = 4(y+5)

$x + 5 = 4(y + 5) \\ \implies \: x + 5 = 4y + 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: x = 4y + 15 \: ...........(ii)$

now put the value of x from equation (ii) in equation (i)

$\implies \: 4y + 15 + y = 65 \\ \implies \: 5y = 65 - 15 \: \: \: \: \: \: \: \: \: \\ \implies \: 5y = 50 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: y = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now put the value of y in equation (ii)

$\implies \: x = 4(10) + 15 \\ \implies \: x = 40 + 15 \: \: \: \: \: \\ \implies \: x = 55 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

since, value of y is 10 and x is 55

so age of anu = 55 years

and age of binu = 10 years

Answer 2

refer to the attachment above.........