Question

Q71. Ten years ago, the ratio of the ages of a father and his son was 5:3. Five years from now, the ratio of their respective ages
will be 3: 2. Find the sum of their present ages.
Oa) 120
Ob) 140
Oc) 150
Od) 160​

Answer 1

Answer:

answer is 120. hope this is write

Answer 2

Given:-

• Ten years ago, the ratio of the ages of a father and his sone was 5:3
• Five years from now, their ages will be in the ratio 3:2

To Find:-

• Sum of their present ages

Assumption:-

• Let the age of father be x
• Age of son be y

Solution:-

If the present ages of father and his son is x and y respectively then,

10 years ago,

• Age of father = x - 10
• Age of son = y - 10

Hence,

(x - 10) : (y - 10) = 5 : 3

⇒ (x - 10)/(y - 10) = 5/3

By cross - multiplying,

⇒ 3(x - 10) = 5(y - 10)

⇒ 3x - 30 = 5y - 50

⇒ 3x - 5y = - 50 + 30

⇒ 3x - 5y = -20 ⟶ (i)

Now,

After 5 years,

• Age of father = x + 5
• Age of son = y + 5

Hence,

(x + 5) : (y + 5) = 3 : 2

⇒ (x + 5)/(y + 5) = 3/2

By - cross multiplication,

⇒ 2(x + 5) = 3(y + 5)

⇒ 2x + 10 = 3y + 15

⇒ 2x - 3y = 15 - 10

⇒ 2x - 3y = 5 ⟶ (ii)

Now we have,

3x - 5y = -20 ⟶ (i)

2x - 3y = 5 ⟶ (ii)

Multiply equation (i) by 2 and equation 2 by 6

The equations go like this:-

• 3x - 5y = -20 ⟶ (i) × 2
• 2x - 3y = 5 ⟶ (ii) × 3

= 6x - 10y = -40 ⟶ (iii)

= 6x - 9y = 15 ⟶ (iv)

Subtracting equation (iii) and (iv)

= (6x - 10y) - (6y - 9y) = -40 - 15

⇒ 6x - 10y - 6c + 9y = -55

⇒ 6x - 6x - 10y + 9y = -55

⇒ -y = -55

⇒ y = 55

Putting the value of y in equation (i)

= 3x - 5y = -20

⇒ 3x - 5 × 55 = -20

⇒ 3x - 275 = -20

⇒ 3x = -20 + 275

⇒ 3x = 255

⇒ x = 255/3

⇒ x = 85

Therefore,

• Present age of father = x = 85 years
• Present age of son = y = 55 years

Let us find the sum of their ages,

= 85 + 55

= 140

∴ The sum of present age of father and son is 140 years [Option (b)]

________________________________