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If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now

Solution:

Given, Zeba was younger by 5 years than her original age.

We have to find the present age of Zeba.

Let the present age of Zeba be x years.

Before 5 years, age of Zeba = (x - 5) years.

As per given condition,

(x - 5)² = 5x + 11

By using algebraic identity,

(a - b)² = a² - 2ab + b²

(x - 5)² = x² - 10x + 25

So, x² - 10x + 25 = 5x + 11

x² - 10x + 25 - 5x - 11 = 0

By grouping,

x² - 10x - 5x + 25 - 11 = 0

x² - 15x + 14 = 0

On factoring,

x² - 14x - x + 14 = 0

x(x - 14) - 1(x - 14) = 0

(x - 1)(x - 14) = 0

Now, x - 1 = 0

x = 1

Also, x - 14 = 0

x = 14.

Since, the present age cannot be 1.

Therefore, the present age of Zeba is 14 years.

✦ Try This: If Samina were younger by 7 years than what she really is, then the square of her age (in years) would have been 13 more than five times her actual age. What is her age now

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 5

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now

Summary:

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. The present age of Zeba is 14 years

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