Question

A cake chain manufactures two types of products: cakes/pastries/gateaux, and savouries. The chain was concerned about high wastage (in terms of leftover) and wanted to reduce it. The table below gives sales, costs and leftover (as a percentage of sales) for both product lines from 1993 to 2004.

If profit = sales - cost - leftover, in which of these years was the cake chain in losses (leftover here means the leftover amount, not the percentage)?

1. 1993
2. 1997
3. 1998
4. 2000

Choose the right option:

• A. 1, 2, 3, 4
• B. 3, 4
• C. 2, 3
• D. 1, 2, 3

Hint:

Convert each year's leftover percentage into an actual amount, then check whether sales cover cost plus that leftover.

Answer 1

The Correct Option is A

Step 1: Set up the profit formula.
Profit for a year is sales minus cost minus leftover, where leftover here means the leftover amount in Rs. lac, not the percentage figure printed in the table.
To get the leftover amount for a year, multiply the leftover percentage by that year's sales and divide by 100. The chain's total profit in a year is the cakes line profit plus the savouries line profit.

Step 2: Check 1993.
Cakes: sales 81.47, cost 80.06, leftover = 1.52% of 81.47 = 1.24. Profit = 81.47 - 80.06 - 1.24 = 0.17.
Savouries: sales 41.79, cost 41.07, leftover = 9.38% of 41.79 = 3.92. Profit = 41.79 - 41.07 - 3.92 = -3.20.
Total profit for 1993 = 0.17 - 3.20 = -3.03 lac, a loss.

Step 3: Check 1997.
Cakes: sales 886.71, cost 865.69, leftover = 1.06% of 886.71 = 9.40. Profit = 886.71 - 865.69 - 9.40 = 11.62.
Savouries: sales 516.32, cost 511.10, leftover = 8.29% of 516.32 = 42.80. Profit = 516.32 - 511.10 - 42.80 = -37.58.
Total profit for 1997 = 11.62 - 37.58 = -25.96 lac, a loss.

Step 4: Check 1998.
Cakes: sales 936.52, cost 926.06, leftover = 1.74% of 936.52 = 16.30. Profit = 936.52 - 926.06 - 16.30 = -5.84.
Savouries: sales 466.19, cost 464.60, leftover = 11.04% of 466.19 = 51.49. Profit = 466.19 - 464.60 - 51.49 = -49.90.
Total profit for 1998 = -5.84 - 49.90 = -55.74 lac, a loss.

Step 5: Check 2000.
Cakes: sales 752.09, cost 743.20, leftover = 1.50% of 752.09 = 11.28. Profit = 752.09 - 743.20 - 11.28 = -2.39.
Savouries: sales 637.63, cost 630.09, leftover = 5.61% of 637.63 = 35.78. Profit = 637.63 - 630.09 - 35.78 = -28.24.
Total profit for 2000 = -2.39 - 28.24 = -30.63 lac, a loss.

Final Answer:
All four years, 1993, 1997, 1998 and 2000, come out with a negative total profit once the leftover amount is subtracted along with cost, so the chain was in losses in every one of them.
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