Question

Ratio of present ages of Sona and Sonali is 5:3. After 5 years their ages will be in the ratio 10:7. Calculate the present ages.​

Answer 1

Required answer:-

Question:

Ratio of present ages of Sona and Sonali is 5:3. After 5 years their ages will be in the ratio 10:7. Calculate the present ages.

Solution:

Given,

• Ratio of present ages of Sona and Sonali = 5 : 3

• Ratio of their ages after 5 years = 10 : 7

To find:

• Present ages of Sona and Sonali

Assumptions:

• Let present age of Sona be 5x

• Let present age of Sonali be 3x

Concept:

• Simultaneous equations

Steps of solving

1. Assume a variable (unknown) eg., x

2. According to the given statement, setup the two equations in term of x

3. Solve the equations.

Step by step explaination:

➪ After assuming their present ages.

According to the question.

➪ $\frac{5x + 5}{3x + 5} = \frac{10}{7}$

After cross multiplying....

➪ 35x + 35 = 30x + 50

➪ 35x - 30x = 50 - 35

➪ 5x = 15

➪ x = 3

Answer:

• Present age of Sona 5x = 5×3 = 15 years

• Present age of Sonali 3x = 3×3 = 9 years

Answer 2

Answer:

So, the ages of Sona & Sonali are 15 years and 9 years respectively.