Question

the difference between the present ages of Trisha and shalini is 14 years. seven years ago, the ratio of their ages was 5:7 respectively. what is shalini present age?

Answer 1

Let T and S are respective ages.
T-S =14.......(equ 1)

(T-7):(S-7) = 7:5

5(T-7) = 7(S-7)

5T-7S= -14........(equ2)

Solve equ2 and equ1

You will get T =56 and S =42

Answer 2

Present age of Shalini = 56 years

Given :

• The difference between the present ages of Trisha and shalini is 14 years.

• Seven years ago, the ratio of their ages was 5 : 7 respectively.

To find :

Present age of Shalini

Solution :

Step 1 of 2 :

Form the equation to calculate the present age of Shalini

Here it is given that Seven years ago, the ratio of their ages was 5 : 7 respectively.

Let us assume that Seven years ago, the ages of Trisha and shalini was 5x years and 7x years respectively

∴ Present ages of Trisha and shalini is (5x + 7) years and (7x + 7) years respectively

Now it is given that the difference between the present ages of Trisha and shalini is 14 years.

By the given condition

$\displaystyle \sf (7x + 7) - (5x + 7) = 14$

Step 2 of 2 :

Calculate present age of Shalini

$\displaystyle \sf (7x + 7) - (5x + 7) = 14$

$\displaystyle \sf{ \implies }7x + 7 - 5x - 7 = 14$

$\displaystyle \sf{ \implies }2x = 14$

$\displaystyle \sf{ \implies }x = \frac{14}{2}$

$\displaystyle \sf{ \implies }x = 7$

∴ Present ages of Trisha and Shalini is 42 years and 56 years respectively

Hence present age of Shalini = 56 years

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