Priya, Quentin and Ravi shared a pack of cards. Priya took 50 cards first. Quentin then took 16 of the remaining cards and Ravi took the rest. The number of cards Ravi took was 58 of the total number of cards. How many more cards did Ravi take than Quentin?
- 25
- 75
- 100
- 125
Need a hint?
Find the total first. Ravi's share is 56 of what is left after Priya, and it is also 58 of the total, so compare the two.
Worked answer
- Let the total be T. The remaining cards are T - 50.
- Quentin takes 16 of the remaining, so Ravi takes 56 of the remaining.
- Ravi's cards = 58 of T = 56 of the remaining, so the remaining = 68 of T = 34 of T.
- So Priya's 50 cards = T - 34 of T = 14 of T, giving T = 200.
- Remaining = 150, so Quentin takes 150 ÷ 6 = 25 and Ravi takes 150 - 25 = 125.
- Ravi took 125 - 25 = 100 more cards than Quentin.
Answer: 100 cards
The mistake this question tests
Habit
Fraction of a remainder
Pupils often stop at Ravi's 125 cards, or subtract Priya's 50 instead of Quentin's 25, forgetting the question asks for the difference between Ravi and Quentin.
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