Question

The sum of a ages of a father and son is 45 years. Five years ago the product of their ages was four times the father age at that time. The present age of father and sons respectively are? (a) 25 years. 5 year (b) 36 years, 9 year (c) 39 years. 4 year (d) None of these​

Answer 1

G I V E N :

The sum of a ages of a father and son is 45 years. Five years ago the product of their ages was four times the father age at that time. The present age of father and sons respectively are?

(a) 25 years, 5 years

(b) 36 years, 9 years

(c) 39 years, 4 years

(d) None of these

S O L U T I O N :

Let us assume ⤵

Father's age be a

Son's age be b

According to the question,

Sum of father's age and son's age is 45

Hence, the equation is :

• a + b = 45

• b = 45 - a

Five years before ⤵

Father's age was a - 5

Son's age was b - 5

Now, given that product of their ages was four times the father age at that time

So,

$\twoheadrightarrow \red{\frak{(a - 5)(b - 5) = 4(a - 5)}}$

Putting b = 45 - a we get

$\twoheadrightarrow \frak{ \red{(a - 5)(45 - a - 5) = 4(a - 5)}}$

$\twoheadrightarrow \frak{ \red{(a - 5)(40 - a) = 4a - 20}}$

$\twoheadrightarrow \frak{ \red{a(40 - a) - 5(40 - a) = 4a - 20}}$

$\twoheadrightarrow \frak{ \red{40a - {a}^{2} - 200 + 5a = 4a - 20}}$

$\twoheadrightarrow \frak{ \red{45a - {a}^{2} - 180 = 4a }}$

$\twoheadrightarrow \frak{ \red{41a - {a}^{2} - 180 = 0 }}$

$\twoheadrightarrow \frak{ \red{ {a}^{2} - 41a + 180 = 0}}$

$\twoheadrightarrow \frak{ \red{(a - 36)(a - 5) = 0}}$

Now, we get two conditions

1st Condition :

• a - 36 = 0

• a = 36

2nd Condition :

• a - 5 = 0

• a = 5

Now, we know that someone's father's age cannot be 5

So, 5 will be rejected and 36 will be accepted

• Father's age = a = 36 years

• Son's age = 45 - a = 45 - 36 = 9 years

☞ Father's age is 36 years and son's age is 9 years

• HENCE, OPTION B IS CORRECT

Answer 2

Answer:

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Step-by-step explanation:

let the present ages of father and son be x and y years respectively

so according to first condition

x+y=45 (1)

according to second condition

(x-5)(y-5)=4(x-5)

y-5=4

ie y=9

substitute value of y in (1)

we get

x=36

Hence present age of father is 36 years and that of his son is 9 years