Question

Mrs tandon has two sons one being exactly one year older than the other .At present her age is equal to sum of squares of ages of her sons.if 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons

Answer 1

Hi, Its ad714 to answer you.

First of all,let me tell you that this is one of the most tricky question that I had ever answered.

SOLUTION:
Let the age of Mrs Tandon be y
and x and x+ 1 be the age of her two sons

So, according to the Question.

y=(x)²+(x+1)²
y=x²+x²+1+2x
y=2x²+2x+1
$y = 2x ^{2} + 2x + 1$
eqn no. 1

Also,
y+4=(x+1+4)5
(because after 4 years miss is turned on stage will be 5 times equal to the age of her elder son)

y+4=(x+5)5
y+4=5x+25
y=5x+21


$y = 5x + 21$
eqn no. 2

Now, from equation (1) and (2).

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Answer 2

Answer:

Let , the age of elder son be "x".

Then the age younger son = x -1.

given that,

Tendon 's age is equal to the sum of

squares of her two son's.

So, tendon 's age = (x)² +(x - 1)²

= x² + x² + 1² - 2x

Tendon 's age = (2x² - 2x + 1 .) years.-- eq-(1)

And also given that, in 4 years her age will be 5 times the age of the eldest son.

After 4 years , Elder son's age = x + 4.

Tendon's age = 5(x + 4)

Tendon's age = (5x + 20) years.-- eq-(2)

From eq -(1) ,

Tendon's age after 4 years = (2x² - 2x +1 ) + 4

Tendon's age = 2x²- 2x +5 -- eq- (3)

Equate eq (2) & (3).

5x + 20 = 2x² - 2x + 5

2x² - 2x +5 - 5x - 20 = 0

2x² - 7x - 15 = 0

2x² - 10x + 3x - 15 = 0

2x ( x - 5) + 3(x - 5) = 0

(2x + 3)(x - 5) = 0

2x + 3 = 0

2x = -3

x = -3/2.

x - 5 = 0

x = 5.

Age of a person cannot be negative so Positive value is taken.

Hence, x = 5.

Therefore, Age of elder son = x = 5 years and age of younger son = (x - 1) = (5-1) = 4 years.

Step-by-step explanation: