The ratio between the present age of Akash and Vipul is 5:4. The ratio between Akash's age 10 years hence and Vipul's age 10 years ago is 5:3. What is the ratio between Akash's age 5 years ago and Vipul's age 5 year hence?
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let x and y be the present age of Akash and Vipul. then,
x÷ y=5÷4
i.e.4x=5y(by cross multiplication)
so x=5y÷4
again x+10÷y-10=5÷3
i.e.3x+30=5y-50
substituting the value of x we get
3(5y÷4)+30+50=5y
i.e. 80=5y-3(5y÷4)
i.e. 80=5y-(15y÷4)
i.e. 80=(20y-15y)÷4
i.e. 320=5y
so y=64
and x=(5×64)÷4
=80
now the required ratio=(x-5)÷(y+5)
=75÷69
=25÷23
x÷ y=5÷4
i.e.4x=5y(by cross multiplication)
so x=5y÷4
again x+10÷y-10=5÷3
i.e.3x+30=5y-50
substituting the value of x we get
3(5y÷4)+30+50=5y
i.e. 80=5y-3(5y÷4)
i.e. 80=5y-(15y÷4)
i.e. 80=(20y-15y)÷4
i.e. 320=5y
so y=64
and x=(5×64)÷4
=80
now the required ratio=(x-5)÷(y+5)
=75÷69
=25÷23
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