Question

Five years ago, the ratio of ages of Pravin and his sister was 3:1. Two years
hence, it will be 5:4. Find their present ages​

Answer 1

Answe: 8 and 6

Step-by-step explanation:

Five years ago: 3x/x         (Ratio can be written in way of division)

Present: 3x+5/x+5    

Future: 3x+7/x+7

Future also given: 5/4  (Simplified without 'x')

Thus, 3x + 7/x +7 = 5/4

After cross-multiplying : 12x + 28 = 5x + 35

                                        7x = 7

                                         x = 1

Now we now that present ages are 3x+5/x+5 so after replacing x with one we get: 3 + 5 : 1 + 5  = 8 : 6. Thus Pravin is 8 and his sister is 6

Hope you understood.

All we need to do here is find two plausible expression including x of the futures ratio and form an equation and simplify.

Thanks!

Answer 2

Given,

Before 5 years,

• The Ratio of ages of Pravin and his sister was 3 : 1.

2 years hence,

• The Ratio of ages of Pravin and his sister become 5 : 4.

To Find,

• The Present Age of Pravin and his sister.

Solution,

Before 5 years,

Let's,

The Age of Pravin = 3X

So,

The Age of his sister = X

After 2 years,

The Age of Pravin = 3X + 5 + 2 = 3X + 7

The Age of his sister = X + 5 + 2 = X + 7

The Ratio of Their Ages = 5 : 4

→ 3X + 7 : X + 7 = 5 : 4

→ (3X + 7)/(X + 7) = 5/4

→ 4 × (3X + 7) = 5 × (X + 7)

→ 4 × 3X + 4 × 7 = 5 × X + 5 × 7

→ 12X + 28 = 5X + 35

→ 12X - 5X = 35 - 14

→ 7X = 21

→ X = 21/7

→ X = 3

The Present Age of Pravin = 3X + 5

→ The Present Age of Pravin = 3(7) + 5

→ The Present Age of Pravin = 21 + 5

→ The Present Age of Pravin = 26 years

The Present Age of his sister = X + 5

→ The Present Age of his sister = 7 + 5

→ The Present Age of His Sister = 12 years

Required Answer,

• The Age of Pravin = 26 years
• The Age of His Sister = 12 years