Canteen Combo Reconciliation
The school canteen in Hubballi sells idli plates and vadas as separate items. On Monday, 3 idli plates and 2 vadas were sold for ₹220. On Tuesday, 2 idli plates and 3 vadas were sold for ₹230. Prices did not change between the two days. On Wednesday, 4 idli plates and 7 vadas were sold, and the cash box showed ₹540. The canteen manager, who is a parent volunteer, cannot find a bill for a separate item and wants to know whether the Wednesday collection is consistent with the Monday and Tuesday prices. The principal also asks what the Wednesday collection should have been under the same prices, and whether a ₹5 increase in the vada price on Wednesday would explain the figure. Students are asked to solve the price system and then judge the Wednesday discrepancy rather than simply recompute it.
1. Set up and solve the pair of linear equations for the prices of one idli plate and one vada.
Read the worked answer
Let idli plate = i and vada = v. 3i + 2v = 220 2i + 3v = 230
Multiply the first by 3: 9i + 6v = 660. Multiply the second by 2: 4i + 6v = 460. Subtract: 5i = 200, so i = 40. Substitute: 3(40) + 2v = 220 → 120 + 2v = 220 → 2v = 100 → v = 50.
Check: 2(40) + 3(50) = 80 + 150 = 230. Prices are ₹40 per idli plate and ₹50 per vada.
2. Using these prices, check Wednesday's collection of ₹540 and interpret the discrepancy.
Read the worked answer
Expected Wednesday collection = 4(40) + 7(50) = 160 + 350 = ₹510. Cash is ₹540, so there is an excess of ₹30.
This cannot be explained by one extra idli (₹40) or one extra vada (₹50). A ₹30 item outside the two combos, or a recording/change error, is more plausible. Under unchanged prices, the Wednesday collection is not consistent.
3. The manager claims the vada price was raised by ₹5 on Wednesday. Recalculate Wednesday's expected collection and judge whether this explains ₹540.
Read the worked answer
If the vada price rose to ₹55, expected collection = 4(40) + 7(55) = 160 + 385 = ₹545.
The cash of ₹540 would then be ₹5 short, not ₹30 excess. A ₹5 increase explains a small shortfall but not the observed excess, so it is not a consistent explanation of ₹540.