If Ram purchases a fan, he gets 8% discount, however, if he purchases three fans he gets 6% on the first, 10% on the second and 12% on the third. If the price paid by the Ram for three fans is ₹6,800, then what will be the marked price of each fan?
- (a)₹2,550
- (b)₹2,500
- (c)₹2,400
- (d)₹2,450
Answer
Why
Correct — B. The question asks for the marked price of each fan and offers one figure, so all three fans carry the same marked price M. Only the discount rates differ.
Fan 1 at 6% off: 0.94M
Fan 2 at 10% off: 0.90M
Fan 3 at 12% off: 0.88M
These are three separate articles, so the amounts add:
0.94M + 0.90M + 0.88M = 2.72M
2.72M = 6800
M = 6800 ⁄ 2.72 = ₹2,500 → option (b).
The 8% rate never enters the calculation — it applies only to buying a single fan.
Why the others are wrong
- (a)₹2,550 — ₹2,550 overshoots. Three fans marked at ₹2,550 with 6%, 10% and 12% off cost 2.72 × 2,550 = ₹6,936, which is ₹136 more than the ₹6,800 actually paid.
- (c)₹2,400 — ₹2,400 falls short. 2.72 × 2,400 = ₹6,528, which is ₹272 below the amount paid. The marked price has to be higher than this.
- (d)₹2,450 — ₹2,450 still falls short, at 2.72 × 2,450 = ₹6,664. Only ₹2,500 makes 2.72M land exactly on ₹6,800, so this is a near miss rather than an alternative reading.
Concept
A d% discount means you pay (100 − d)% of the marked price, so a 6% discount is a factor of 0.94.
The distinction the question is built on: three separate articles add, one article with successive discounts multiplies. Here the three fans are three purchases, so the payment is 0.94M + 0.90M + 0.88M = 2.72M.
Had all three rates been applied one after another to a single fan, the factor would be 0.94 × 0.90 × 0.88 = 0.74448 — a completely different number, and a completely different question.
The 8% figure is a decoy describing the one-fan purchase, which Ram did not make. The stem also never states that the fans are identically priced, but it asks for the marked price of each fan and offers single values, which forces that reading.
Key facts
- Paying after a d% discount means paying (100 − d)% of the marked price.
- Discounts on separate articles add as amounts: 0.94M + 0.90M + 0.88M = 2.72M.
- Successive discounts on one article multiply: 0.94 × 0.90 × 0.88 = 0.74448.
- 6,800 ⁄ 2.72 = 2,500, so each fan is marked at ₹2,500.
Study next
Common traps
- Multiplying 0.94, 0.90 and 0.88 as though the rates were successive on one fan.
- Applying the 8% rate, which the stem offers only for a single-fan purchase.
- Reading ₹6,800 as the price of one fan rather than of all three.
SSC also sets the chain on a single article, where the factors multiply rather than add: 12 Sep 2024, 09:00, Quant Q.2 (₹5,000 at 20%, 15% and 10%) and 19 Sep 2024, 16:00, Quant Q.20 (a ₹12,500 cooker at 6%, 6% and 4%).
23 Sep 2024, 16:00, Quant Q.21 and 25 Sep 2024, 16:00, Quant Q.24 ask only for the single equivalent discount. Before computing, read the stem to see whether the rates sit on one article or on several.
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