Question

The sum of present ages of ram and mohan is 60 years.in eight years ram will be five years older than three times as old as mohan was thee years ago.find the present ages

Answer 1

let the prsnt age of ram be 'x' yrs and mohan's be 'y'yrs

CASE 1

x+y=60. -(eq.1)

CASE 2

x+8=3(y-3)+5

=3y-9+5

=3y-4

x-3y+12=0. -(eq.2)

subtracting (1) from (2), we get,

-4y= -72

y=18

substituting value of y in eq 1

x+18=60

x=60-18

=42

therefore,

age of ram is 42 yrs

age of mohan is 18 yrs

Answer 2

Concept

After reading the age problem, say "X", assuming the unknown age is a variable.  Convert the problem statement into a formula.  Solve equations to calculate variables. The value obtained  must satisfy the conditions specified in the task.

Given

We have been given that the sum of present ages of Ram and Mohan is 60 years and after 8 years Ram will be five years older than three times as old as Mohan was three years ago.

Find

We are asked to determine the present age of Ram and Mohan .

Solution

Let the present age of Ram be x years .

Let the present age of Mohan be y years .

According to the statement "the sum of present ages of Ram and Mohan is 60 years " equation will be

$x+y=60$   ...(1)

Now, according to the statement "in eight years Ram will be five years older than three times as old as Mohan was thee years ago" equation will be

$x+8=3(y-3)+5\\x+8=3y-9+5\\\x+8=3y-4\\x-3y=-12$ ......(2)

Putting the value of x from equation (1) in equation (2) , we get

$60-y-3y=-12\\-4y=-72\\y=18$

From equation (1) $x=60-18=42$

Therefore, the present age of Ram and Mohan are 42 years and 18 years respectively .

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