A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount.
- 5,640
- 6,840
- 6,768
- 7,008
Sol:
A person divides a certain amount among his three sons in the ratio = 3 ∶ 4 ∶ 5
If he had divided this amount in the ratio = 1/3 ∶ 1/4 ∶ 1/5
The person who had got the lowest share earlier would get Rs. 1,188 more
Calculations:
A person divides a certain amount among his three sons in the ratio = 3 ∶ 4 ∶ 5
Let money get by first, second and third son be 3x, 4x and 5x respectively
Total share = 3x + 4x + 5x = 12x
Here first son got minimum share i.e 3x
If person had divided total amount in the ratio = 1/3 ∶ 1/4 ∶ 1/5
LCM of 3, 4 and 5 = 60
Ratio of First, second and third = (1/3) × 60 ∶ (1/4) × 60 ∶ (1/5) × 60
⇒ 20 ∶ 15 ∶ 12
Share of first son = (20/47) × Total share
Share of first son = (20/47) × 12x
⇒ 240x/47
According to the question
⇒ (240x/47) – (3x) = 1188
⇒ (240x – 141x)/47 = 1188
⇒ 99x/47 = 1188 ⇒ x = 12 × 47
⇒ x = 564
Total amount = 12x
⇒ 12 × 564 = Rs. 6768
∴ The total amount is Rs. 6768
