Question

Three persons A, B, C had different amount of money with them. C had an amount equal to the average of their total. A spent half of his money, B spent 2 / 3 of his money and C spent all of his money. The remaining amount with them is equal to half the amount B initially have. The percentage of total amount spent by all together, is:
1. 50%
2. 75%
3. 80%
4. 90%

Answer 1

Correct Answer - Option 2 : 75%

Given 

A spent = 1/2 of his money 

B spent = 2/3 of his money 

Formula Used 

Percentage = (actual/total) × 100 

Calculation 

Let the initial amount of A, B and C be a, b, and c respectively 

According to question 

⇒ c = (a+ b + c)/3 

Then 2c = a + b

Total expenditure = a/2 + 2b/3 + c

A's remaining amount = a/2 

B' remaining amount = b/3 

C's remaining amount = 0 

Remaining = a/2 + b/3

According to the question,

⇒ a/2 +b/3 = b/2

⇒ a/2 = b/6

⇒ a/b = 1/3

Take a = 1 b = 3 then, c = 2

Total expenditure = 1/2 + 2 + 2 = 9/2

Percentage = 9/(2 × 6) × 100 = 75%

∴ The percentage of total amount spent by all together is 75%