A box contained mango, pear, and orange sweets. 3/5 of the sweets were mango. Of the remaining sweets, 2/3 were pear and the rest were orange. Priya gave away some mango sweets. After this, 2/5 of the sweets in the box were pear. If there were 120 sweets at first, how many mango sweets did Priya give away?
Show Worked Solution
Worked Solution
Step 1: Find the original number of each type of sweet.
Mango = 3/5 × 120 = 72.
Remaining = 120 − 72 = 48.
Pear = 2/3 × 48 = 32.
Orange = 48 − 32 = 16.
Step 2: Find the new total after Priya gave away mango sweets.
The number of pear and orange sweets does not change.
After giving away mango, pear = 2/5 of new total.
32 = 2/5 × new total.
New total = 32 × 5/2 = 80 sweets.
Step 3: Find how many mango sweets Priya gave away.
Mango sweets given away = 120 − 80 = 40.
Step 4: Verify.
New mango count = 72 − 40 = 32. Total = 32 + 32 + 16 = 80. Pear fraction = 32/80 = 2/5. Confirmed.
Answer: 40
Correct answer: 40
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