Question

At present Mahesh’s age (in years) is 2 more than the square of his son Varun’s age. When Varun grows to his

father’s present age, Mahesh’s age would be one year less than 10 times the present age of Varun. Using the

above information answer the following questions.

(i) Mahesh’s present age is [1]

(1) 25 years (2) 27 years

(3) 29 years (4) 31 years

(ii) Varun’s age after 4 years is [1]

(1) 5 years (2) 7 years

(3) 9 years (4) 11 years

(iii) Difference between the present ages of Mahesh and Varun is [1]

(1) 10 years (2) 24 years

(3) 22 years (4) 25 years

(iv) Sum of present ages of Mahesh and Varun is [1]

(1) 30 years (2) 32 years

(3) 35 years (4) 37 years​

Answer 1

Answer:

Question no. 11 of FST 04 Maths of aakash institute. Heheh ;)

Solve by your own

Answer 2

Mahesh’s present age is 27 years

Varun’s age after 4 years is 9 years

Difference between the present ages of Mahesh and Varun is 22 years

Sum of present ages of Mahesh and Varun is 32 years

Given : Mahesh's age at present is 2 more than the square of his son Varun's age

When Varun grows to his father’s present age, Mahesh’s age would be one year less than 10 times the present age of Varun.

To Find :  (i) Mahesh’s present age is

(1) 25 years (2) 27 years

(3) 29 years (4) 31 years

(ii) Varun’s age after 4 years is

(1) 5 years (2) 7 years

(3) 9 years (4) 11 years

(iii) Difference between the present ages of Mahesh and Varun is

(1) 10 years (2) 24 years

(3) 22 years (4) 25 years

(iv) Sum of present ages of Mahesh and Varun is

(1) 30 years (2) 32 years

(3) 35 years (4) 37 years​

Solution : Let at present Varun's age is x

so Mahesh's age will be 2 more than the square of his son Varun’s age i.e. 2 + $x^{2}$

When Varun's age is 2 + $x^{2}$  Mahesh's age will be 10(x) -1

Now  10(x) -1 - (2 + $x^{2}$) = 2 + $x^{2}$ - x

10x -3 - $x^{2}$ -2 - $x^{2}$ + x = 0

-5 -2 $x^{2}$+11x = 0

= $2x^{2} -11x+5$ = 0

(2x-1) (x-5) = 0

x = 5 and x = $\frac{1}{2}$

So x is 5

Varun's present age is 5 years

i ) So Mahesh present age will be 2 + 25 = 27 years

So option 2) is correct.

ii) Varun's age after 4 year will be 5 +4 = 9 year

So option 3) is correct.

iii) Present age of Mahesh is 27 years

Present age of Varun is 5 years

Difference between the present ages of Mahesh and Varun is 27 - 5 = 22 years

So option 3) is correct

iv) Present age of Mahesh is 27 years

Present age of Varun is 5 years

Sum of present ages of Mahesh and Varun is 27 +5 = 32 years

So option 2) is correct.

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