A neighbourhood bakery makes four items every morning – Bread (loaves), Buns, Croissants and Muffins. Whatever is not sold by closing time is thrown away (wastage). The first table gives the number of units produced on each day of a particular week; the second gives the number of units wasted. Two entries of the wastage table are missing and are marked *x* and *y*.
Units produced
| Item | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| Bread | 120 | 100 | 110 | 130 | 150 |
| Buns | 200 | 180 | 220 | 200 | 250 |
| Croissants | 60 | 50 | 70 | 60 | 80 |
| Muffins | 90 | 80 | 100 | 90 | 120 |
Units wasted
| Item | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| Bread | 12 | 5 | 11 | 13 | 6 |
| Buns | 20 | 27 | 22 | x | 25 |
| Croissants | 6 | 2 | 14 | 3 | y |
| Muffins | 9 | 16 | 5 | 9 | 12 |
The cost of production and the selling price per unit are:
| Item | Cost (Rs) | Price (Rs) |
|---|---|---|
| Bread | 20 | 35 |
| Buns | 8 | 15 |
| Croissants | 25 | 50 |
| Muffins | 15 | 30 |
Additional information:
- The total number of buns wasted during the week was 104.
- On Friday, the total number of units wasted (all four items together) was exactly 8.5% of the total number of units produced that day.
Wastage rate = units wasted ÷ units produced. Profit on a day = (units sold × price) − (units produced × cost), where units sold = produced − wasted.
Units produced
| Item | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| Bread | 120 | 100 | 110 | 130 | 150 |
| Buns | 200 | 180 | 220 | 200 | 250 |
| Croissants | 60 | 50 | 70 | 60 | 80 |
| Muffins | 90 | 80 | 100 | 90 | 120 |
Units wasted
| Item | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| Bread | 12 | 5 | 11 | 13 | 6 |
| Buns | 20 | 27 | 22 | x | 25 |
| Croissants | 6 | 2 | 14 | 3 | y |
| Muffins | 9 | 16 | 5 | 9 | 12 |
The cost of production and the selling price per unit are:
| Item | Cost (Rs) | Price (Rs) |
|---|---|---|
| Bread | 20 | 35 |
| Buns | 8 | 15 |
| Croissants | 25 | 50 |
| Muffins | 15 | 30 |
Additional information:
- The total number of buns wasted during the week was 104.
- On Friday, the total number of units wasted (all four items together) was exactly 8.5% of the total number of units produced that day.
Wastage rate = units wasted ÷ units produced. Profit on a day = (units sold × price) − (units produced × cost), where units sold = produced − wasted.
Question 1
Single correct option
On which day was the overall wastage rate (all four items taken together) the highest?
- A. Monday
- B. Tuesday
- C. Wednesday
- D. Friday
Show answer and solution
Answer: (B) Tuesday
Daily totals: Mon 47/470 = 10.0%; Tue (5 + 27 + 2 + 16) = 50/410 ≈ 12.2%; Wed 52/500 = 10.4%; Thu (13 + 10 + 3 + 9) = 35/480 ≈ 7.3%; Fri 51/600 = 8.5%.
Tuesday is the highest. It has the lowest production but the second-highest wastage in absolute terms.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
Tuesday is the highest. It has the lowest production but the second-highest wastage in absolute terms.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
Question 2
Numerical answer
For how many of the 20 item–day combinations did the wastage exceed 10% of that day's production of the item?
Show answer and solution
Answer: 3
Compare each wasted figure with one-tenth of production (strictly greater):
- Bread: 12 = 10% of 120, 13 = 10% of 130, 11 = 10% of 110 – none exceed.
- Buns: Tue 27 > 18 ✓; Mon 20, Wed 22 equal 10%; Thu x = 10 < 20; Fri 25 = 10%.
- Croissants: Wed 14 > 7 ✓; Mon 6 = 10%; Fri y = 8 = 10% (not more).
- Muffins: Tue 16 > 8 ✓; Mon 9 = 10%, Thu 9 = 10%.
Answer = 3 (Buns–Tue, Croissants–Wed, Muffins–Tue).
Trap: many cells are exactly 10%; 'exceed' excludes them.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
- Bread: 12 = 10% of 120, 13 = 10% of 130, 11 = 10% of 110 – none exceed.
- Buns: Tue 27 > 18 ✓; Mon 20, Wed 22 equal 10%; Thu x = 10 < 20; Fri 25 = 10%.
- Croissants: Wed 14 > 7 ✓; Mon 6 = 10%; Fri y = 8 = 10% (not more).
- Muffins: Tue 16 > 8 ✓; Mon 9 = 10%, Thu 9 = 10%.
Answer = 3 (Buns–Tue, Croissants–Wed, Muffins–Tue).
Trap: many cells are exactly 10%; 'exceed' excludes them.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
Question 3
Numerical answer
What was the bakery's total profit (in Rs) on Friday?
Show answer and solution
Answer: 6455
Friday (with y = 8):
- Bread: sold 144 × 35 = 5,040; cost 150 × 20 = 3,000 ⇒ 2,040
- Buns: sold 225 × 15 = 3,375; cost 250 × 8 = 2,000 ⇒ 1,375
- Croissants: sold 72 × 50 = 3,600; cost 80 × 25 = 2,000 ⇒ 1,600
- Muffins: sold 108 × 30 = 3,240; cost 120 × 15 = 1,800 ⇒ 1,440
Total = 2,040 + 1,375 + 1,600 + 1,440 = Rs 6,455.
Shortcut: profit per item = produced × (price − cost) − wasted × price.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
- Bread: sold 144 × 35 = 5,040; cost 150 × 20 = 3,000 ⇒ 2,040
- Buns: sold 225 × 15 = 3,375; cost 250 × 8 = 2,000 ⇒ 1,375
- Croissants: sold 72 × 50 = 3,600; cost 80 × 25 = 2,000 ⇒ 1,600
- Muffins: sold 108 × 30 = 3,240; cost 120 × 15 = 1,800 ⇒ 1,440
Total = 2,040 + 1,375 + 1,600 + 1,440 = Rs 6,455.
Shortcut: profit per item = produced × (price − cost) − wasted × price.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
Question 4
Single correct option
For the week as a whole, which item had the highest wastage rate?
- A. Bread
- B. Buns
- C. Croissants
- D. Muffins
Show answer and solution
Answer: (D) Muffins
Weekly totals:
- Bread: 47/610 ≈ 7.7%
- Buns: 104/1050 ≈ 9.9%
- Croissants: (6 + 2 + 14 + 3 + 8) = 33/320 ≈ 10.3%
- Muffins: 51/480 ≈ 10.6%
Muffins are highest, narrowly ahead of croissants. Note that y must be found first; with y unknown croissants could appear to lead.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
- Bread: 47/610 ≈ 7.7%
- Buns: 104/1050 ≈ 9.9%
- Croissants: (6 + 2 + 14 + 3 + 8) = 33/320 ≈ 10.3%
- Muffins: 51/480 ≈ 10.6%
Muffins are highest, narrowly ahead of croissants. Note that y must be found first; with y unknown croissants could appear to lead.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
Question 5
Single correct option
Suppose that, every day of the week, the bakery had produced exactly as many croissants as it actually sold (with sales unchanged). By how much would the bakery's total profit for the week have increased?
- A. Rs 750
- B. Rs 800
- C. Rs 825
- D. Rs 1,650
Show answer and solution
Answer: (C) Rs 825
Sales (and hence revenue) do not change; only the cost of the wasted croissants is saved.
Weekly croissant wastage = 6 + 2 + 14 + 3 + 8 = 33 units. Saving = 33 × Rs 25 = Rs 825.
Rs 1,650 wrongly uses the selling price (the unsold units never earned revenue); Rs 750 and Rs 800 correspond to 30 and 32 units, i.e. using a wrong value of y (5 or 7) for Friday.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
Weekly croissant wastage = 6 + 2 + 14 + 3 + 8 = 33 units. Saving = 33 × Rs 25 = Rs 825.
Rs 1,650 wrongly uses the selling price (the unsold units never earned revenue); Rs 750 and Rs 800 correspond to 30 and 32 units, i.e. using a wrong value of y (5 or 7) for Friday.
Filling the gaps. Buns: x = 104 − (20 + 27 + 22 + 25) = 10. Friday production = 150 + 250 + 80 + 120 = 600, so Friday wastage = 8.5% × 600 = 51 ⇒ y = 51 − (6 + 25 + 12) = 8.
| Day | Produced | Wasted | Wastage rate | Profit (Rs) |
|---|---|---|---|---|
| Mon | 470 | 47 | 10.0% | 4,760 |
| Tue | 410 | 50 | 12.2% | 4,050 |
| Wed | 500 | 52 | 10.4% | 4,875 |
| Thu | 480 | 35 | 7.3% | 5,175 |
| Fri | 600 | 51 | 8.5% | 6,455 |
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