Question

Sheila and her brother Mohan have their ages in the ratio 5:7. Four years from now their ages will be in the ratio 3:4.Find their present ages. Who is elder among them and by how many years?

Answer 1

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Answer 2

Given - Present ages and age after four years

Find - Elder among them

Solution - Mohan is elder than Sheila by 8 years.

Let the present ages of Sheila and Mohan be 5x and 7x. Let the ages of Sheila and Mohan after four years be 3x and 4x.

After four years,

The age of Sheila = 5x + 4

The age of Mohan = 7x + 4

Now, as per the question, the ages of Sheila and Mohan after four years are 3x and 4x.

So,

$\frac{5x + 4}{7x + 4} = \frac{3x}{4x}$

Cross multiplying -

20x² + 16x = 21x² + 12x

16x - 12x = 21x² - 20x²

x² = 4x

x = 4

So, age of Sheila is 5x

Age of Sheila = 5*4

Age of Sheila = 20 years

Age of Mohan = 7x

Age of Mohan = 7*4

Age of Mohan = 28 years

Thus, Mohan is elder than Sheila by 8 years.