Math Problem Statement

A had certain number of chocolates. Out of the 60% of the chocolates with A, he gave 80% of the chocolates to B and the remaining to C. If the difference between the number of chocolates left with A and the number of chocolates with B IS 144, then find the total number of chocolates A had.

a) 2000

b) 1500

c) 1600

d) 1800

e) None of these

Solution

Let's solve the problem step by step.

Let the total number of chocolates A initially had be xx.

  1. A gave away 60% of his chocolates: Chocolates given away=0.6x\text{Chocolates given away} = 0.6x This means A has 0.4x0.4x chocolates left.

  2. A gave 80% of the chocolates from the 60% to B: Chocolates given to B=0.8×0.6x=0.48x\text{Chocolates given to B} = 0.8 \times 0.6x = 0.48x

  3. The remaining chocolates from the 60% were given to C: Chocolates given to C=0.6x0.48x=0.12x\text{Chocolates given to C} = 0.6x - 0.48x = 0.12x

  4. The difference between the chocolates left with A and the chocolates with B is 144: Difference=Chocolates with BChocolates left with A\text{Difference} = \text{Chocolates with B} - \text{Chocolates left with A} So, 0.48x0.4x=1440.48x - 0.4x = 144

  5. Simplify the equation: 0.08x=1440.08x = 144 x=1440.08=1800x = \frac{144}{0.08} = 1800

So, the total number of chocolates A had is 1800\boxed{1800}.

Answer: (d) 1800

Would you like more details on this solution or have any other questions?


Here are five related questions:

  1. If A had 2000 chocolates initially, how many would B receive?
  2. What if A gave 90% of his chocolates to B instead of 80%, what would be the new difference?
  3. How many chocolates did C receive in the original problem?
  4. If the difference was 200 instead of 144, what would be the total number of chocolates A had?
  5. If A had initially 2400 chocolates, how many would he have left after giving 60% away?

Tip: Always double-check your percentage calculations, especially when dealing with multiple steps.