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

Step 1: Set up variables for the original numbers.
Let the original number of mangoes in basket A be a, and in basket B be b.

Step 2: Use the first condition.
Moving 10 mangoes from A to B leaves A with \( a-10 \) and B with \( b+10 \), and these become equal.
\[ a - 10 = b + 10 \Rightarrow a - b = 20 \quad \text{...(i)} \]

Step 3: Use the second condition.
Moving 20 mangoes from B to A instead leaves A with \( a+20 \) and B with \( b-20 \), and A becomes twice B.
\[ a + 20 = 2(b - 20) \Rightarrow a + 20 = 2b - 40 \Rightarrow 2b - a = 60 \quad \text{...(ii)} \]

Step 4: Solve equations (i) and (ii) together.
From (i), \( a = b + 20 \). Substitute into (ii):
\[ 2b - (b+20) = 60 \Rightarrow b - 20 = 60 \Rightarrow b = 80 \]

Step 5: Find a.
\[ a = b + 20 = 80 + 20 = 100 \]

Final Answer:
The original number of mangoes in basket A is 100. \[ \boxed{100} \]