Question

Savita is 31. Manish's age 3 years ago
(4) Sum of the present ages of Manish and Savita is 31. Man
was 4 times the age of Savita. Find their present ages.​

Answer 1

Let Manish’s present age be x

Let Savita’s present age be y

(i)

x + y = 31

(ii)

x - 3 = 4(y - 3)

x - 3 = 4y - 12

x - 4y = -9

On solving (i),(ii) we get

x + y = 31

x - 4y = -9

-----------------

 5y = 40

  y = 8

Subtracting y = 8 in (i),

x + y = 31

x + 8 = 31

x = 23.

Therefore:

Manish age = 23 years

Savita age = 8 years

Hope this helps!

Answer 2

Correct Question:

The sum of the present ages of Manish and Savita is 31 years. 3 years ago Manish's age was four times Savita's age at that time. Find their present ages.

Answer:

The present age of Manish is 23 years.

And the present age of Savita is 8 years.

Step-by-step-explanation:

Let Manish's present age be x years.

And Savita's present age be y years.

From the first condition,

$\boxed{x + y = 31}$ ... ( 1 )

3 years ago, Manish's age was ( x - 3 ) years and Savita's age was ( y - 3 ) years.

From the second condition,

x - 3 = 4 ( y - 3 )

∴ x - 3 = 4y - 12

∴ x - 4y = - 12 + 3

∴ $\boxed{x - 4y = - 9}$ ....( 2 )

Subtracting equation ( 2 ) from equation ( 1 ),

x + y = 31 ... ( 1 )

- x - 4y = - 9 ... ( 2 )

_____________

5y = 40

∴ y = $\frac{40}{5}$

∴ $\boxed{y = 8}$

Substituting y = 8 in equation ( 1 ),

x + y = 31

∴ x + 8 = 31

∴ x = 31 - 8

∴ $\boxed{x = 23}$

Ans.: The present age of Manish is 23 years.

And the present age of Savita is 8 years.

Verification:

From the first condition,

x + y = 31

∴ LHS = x + y

∴ LHS = 23 + 8 [ By substituting the values. ]

∴ LHS = 31

RHS = 31

∴ $\boxed{LHS = RHS}$

Now, from second condition,

x - 3 = 4 ( y - 3 )

∴ LHS = x - 3

∴ LHS = 23 - 3 [ By substituting the value. ]

∴ LHS = 20

Now, RHS = 4 ( y - 3 )

∴ RHS = 4 ( 8 - 3 ) [ By substituting the value.]

∴ RHS = 4 ( 5 )

∴ RHS = 4 × 5

∴ RHS = 20

∴ $\boxed{LHS = RHS}$

Hence verified!