Question

There are 2 baskets, A and B, containing mangoes. If 10 mangoes are transferred from A to B, the number of mangoes in both baskets become equal. If 20 mangoes had been transferred from B to A instead, the number of mangoes in basket A would have become twice that in basket B. Find the original number of mangoes in basket A.

• A. 100
• B. 80
• C. 70
• D. 60

Hint:

Set up one equation for each condition using the original number of mangoes in each basket, then solve the two equations together.

Answer 1

The Correct Option is A

Instead of solving two equations together, we can test each answer choice directly against both conditions in the question, since only one value of the original mangoes in basket A can satisfy both conditions at once.

1. 100: If basket A starts with 100, condition 1 (moving 10 from A to B makes the baskets equal) gives $b = a - 20 = 80$. Check condition 2: $a+20 = 120$ and $2(b-20) = 2(60) = 120$. Both sides match, so a = 100 works.
2. 80: This gives $b = 60$ from condition 1. Check condition 2: $a+20 = 100$, but $2(b-20) = 2(40) = 80$. These do not match, so this option fails.
3. 70: This gives $b = 50$ from condition 1. Check condition 2: $a+20 = 90$, but $2(b-20) = 2(30) = 60$. These do not match, so this option fails.
4. 60: This gives $b = 40$ from condition 1. Check condition 2: $a+20 = 80$, but $2(b-20) = 2(20) = 40$. These do not match, so this option fails.

Only a = 100 satisfies both conditions together, so the original number of mangoes in basket A must be 100.

Let's summarize:

• Condition 1 always gives b = a - 20.
• Condition 2 needs a+20 to equal 2(b-20); only a = 100 makes both conditions true at the same time.

So the original number of mangoes in basket A is 100, the same answer reached earlier by solving two equations, this time found by checking each option.