A shopkeeper offers the following schemes on toys of the same marked price.

Question

A shopkeeper offers the following schemes on toys of the same marked price.

(A) Successive discounts of 16% and 29% on any number of toys bought.

(B) Successive discounts of 4%, 34% and 37% on any number of toys bought.

(C) 12% discount on the first 4 toys and 27% discount on each toy thereon.

(D) 4 toys free of cost on buying 10 toys. A customer wants to buy 10 toys.

Which of the above schemes is the least beneficial to her?

1. A. B
2. B. C (Correct answer)
3. C. A
4. D. D

Correct Answer

Option B — C

Detailed Solution & Explanation

The correct answer is C.

Shortcut Trick

• Compare schemes by the fraction of the marked price actually paid — the smallest discount is the least beneficial.
  • (A) $0.84 \times 0.71 = 0.5964 \Rightarrow$ 40.36% off
  • (B) $0.96 \times 0.66 \times 0.63 = 0.3992 \Rightarrow$ 60.08% off
  • (C) on 10 toys: $4$ at 12% off and $6$ at 27% off $\Rightarrow 4(88) + 6(73) = 790$ out of $1000 \Rightarrow$ 21% off
  • (D) buy 10 get 4 free $\Rightarrow$ 14 toys for the price of 10 $\Rightarrow \dfrac{4}{14} =$ 28.57% off
• The smallest discount is 21%, so scheme C is least beneficial.

Alternate Method

• Take the marked price as ₹100 per toy, so 10 toys have a marked price of ₹1,000, and compute what the customer pays under each scheme: A → ₹596.40, B → ₹399.20, C → ₹790, D → ₹1,000 for 14 toys, i.e. ₹714.30 for 10.
• The highest outlay per toy is scheme C, confirming it as the least beneficial.

Additional Information

• "Buy $m$ get $n$ free" is a discount of $\dfrac{n}{m+n}$, not $\dfrac{n}{m}$ — the free items still count in the total received. Here $\dfrac{4}{14} = 28.57\%$, not $40\%$.
• Successive discounts never add. 16% and 29% is not 45% but $16 + 29 - \dfrac{16 \times 29}{100} = 40.36\%$.
• Read the question's direction carefully: it asks for the least beneficial scheme, and the option list here is itself lettered A–D, so the answer key letter and the scheme letter are different things.