Canteen Combo Pricing Consistency
The student council of a Madhyama school runs a small canteen during the annual sports week. On Monday it sold 3 plates of dalma and 2 plates of rice for ₹190. On Tuesday it sold 5 plates of dalma and 3 plates of rice for ₹310. Prices per plate did not change on these two days. On Wednesday the cook proposed a new energy combo of 4 plates of dalma and 1 plate of rice and quoted ₹230. The council has a daily subsidy of ₹1,200 and expects to sell 18 combos on the final day. Before printing the menu, the treasurer wants to know the actual price of each item, whether Wednesday's combo quote is consistent with Monday and Tuesday, and what the council will pay from the subsidy if it sells 18 combos at the corrected combo price.
1. Form two linear equations from Monday and Tuesday sales and solve for the price of one dalma plate and one rice plate.
Read the worked answer
Let d = price of one dalma plate and r = price of one rice plate. 3d + 2r = 190 ...(1) 5d + 3r = 310 ...(2) Multiply (1) by 3 and (2) by 2: 9d+6r=570; 10d+6r=620. Subtract: d=50. Substitute in (1): 150+2r=190, so 2r=40, r=20. Dalma ₹50, rice ₹20.
2. Check whether the Wednesday combo quote of ₹230 is consistent with the prices found.
Read the worked answer
Correct combo price = 4×50 + 1×20 = ₹220. Quoted price = ₹230, so the quote is ₹10 too high. The Wednesday quote is inconsistent with the earlier sales.
3. If 18 combos are sold at the corrected price, how much must students pay after the ₹1,200 subsidy is applied?
Read the worked answer
18 combos at corrected price = 18×220 = ₹3,960. The council pays ₹1,200 from subsidy; students must pay 3,960 − 1,200 = ₹2,760. If the menu used ₹230, students would pay 18×230 − 1,200 = ₹2,940, which is ₹180 more.