10 friends went for dinner and planned to split Rs. 200 equally. 2 didn’t pay. How much did each of the rest pay?
- (a)Rs. 25
- (b)Rs. 20
- (c)Rs. 22
- (d)Rs. 28
Answer
Why
Correct — A.
Rule: the whole bill still has to be paid, so divide it among those who pay.
Payers: 10 − 2 = 8
Each pays: 200 ÷ 8 = Rs. 25 → option (a).
Check: 8 × 25 = 200, the full bill.
Why the others are wrong
- (b)Rs. 20 — Rs. 20 is the planned share, 200 ÷ 10. Eight people paying Rs. 20 each cover only Rs. 160 of the Rs. 200 bill.
- (c)Rs. 22 — Rs. 22 from eight people makes Rs. 176, which leaves Rs. 24 of the bill unpaid.
- (d)Rs. 28 — Rs. 28 from eight people makes Rs. 224, which is Rs. 24 more than the bill.
Concept
Sharing problems turn on what stays fixed. Here the bill, Rs. 200, stays fixed while the number of payers falls from 10 to 8.
When a fixed total is split among fewer people, each share rises. The two non-payers' Rs. 40 is spread over eight people, Rs. 5 each, so Rs. 20 becomes Rs. 25.
The stem does not say in words that the eight covered the whole bill. Rs. 20 answers the other reading, that each paid only the planned share; the key takes the full-bill reading.
Key facts
- Share per payer = total ÷ number of payers.
- The non-payers' Rs. 40, spread over 8 payers, adds Rs. 5 to each share.
- 8 × Rs. 25 = Rs. 200.
Study next
Common traps
- Stopping at the planned share, Rs. 20, without spreading the unpaid part
- Spreading the unpaid Rs. 40 over all 10 friends instead of the 8 who pay
A fixed total is split among fewer people than planned: find the number who pay first, then divide.
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