### A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Rs. 330 for it, how much did it cost to A?

A. Rs. 200 B. Rs. 250 C. Rs. 275 D. Rs. 290 Answer: Option A
First Method Let Cost Price for A was 100 Then CP for B = 100 + 25% of 100 = 125 CP for C = 125 + 20% of 125 = 150 CP for D = 150 + 10% of 150 = 165 But, D pay Rs. 330, Then it must be equal to $\begin{array}{l}165=330\\ 1=\frac{330}{165}\\ 100=\frac{330\times100}{165}=200\\ \text{Thus CP for A = Rs. 200}\end{array}$ Short-cut A’s CP $=330 \times \frac{100}{125} \times \frac{100}{120} \times \frac{100}{110}=\text { Rs. } 200$