Question

Two years ago the ratio of the ages of Manoj and Shyam
was 15:11. Two years hence the ratio of their ages will
be 17:13. What is the present age of Shyam?​

Answer 1

Let the present age of Manoj and Shyam be x years and y years respectively.

Then, two year ago,

x−2/y−2 = 15/11

or, 11x - 22 = 15y - 30

or, 11x - 15y = -8 ... (i)

Again, after two years,

x+2/y+2= 17/13

or, 13x + 26 = 17y + 34

or, 13x - 17y = 8 ... (ii)

Multiplying eqn (i) by 13 and eqn (ii) by 11,

we get

143x - 195y = - 104

- 143 + 187y = - 88

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y = 24 years

Answer 2

• Let present age of Manoj be M and present age of Shyam be N

2 years ago

• Age of Manoj = (M - 2) years

• Age of Shyam = (N - 2) years.

» Two years ago the ratio of the ages of Manoj and Shyam was 15:11.

A.T.Q.

=> $\dfrac{M\:-\:2}{N\:-\:2}\:=\:\dfrac{15}{11}$

Cross-multiply them

=> 11(M - 2) = 15(N - 2)

=> 11M - 22 = 15N - 30

=> 11M - 15N = - 30 + 22

=> 11M - 15N = - 8 ______ (eq 1)

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» Two years hence the ratio of their ages will be 17:13.

A.T.Q.

=> $\dfrac{M\:+\:2}{N\:+\:2}\:=\:\dfrac{17}{13}$

Cross-multiply them

=> 13(M + 2) = 17(N + 2)

=> 13M + 26 = 17N + 34

=> 13M - 17N = 34 - 26

=> 13M - 17N = 8 ______ (eq 2)

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On multiplying (eq 1) with 13 and (eq 2) with 11 we get;

=> 143M - 195N = - 104 _______ (eq 3)

=> 143M - 187N = 88 _______ (eq 4)

• Subtract (eq 4) from (eq 3)

=> 143M - 195N - (143M - 187N) = - 104 - 88

=> - 195N + 187N = - 192

=> -8N = - 192

=> N = 192/8

=> N = 24

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Present age of Shyam = 24 years (N)

__________ [ ANSWER ]

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