The table below gives the sales (in ₹ crore) of a consumer-goods company in 2015, for four product categories across five regions. Some entries have been smudged and are shown as '?'. The row totals and the column totals are correct.
| Region | Soaps | Shampoos | Toothpaste | Detergents | Total |
|---|---|---|---|---|---|
| North | 120 | 80 | 60 | 140 | 400 |
| South | 150 | 110 | 90 | 100 | 450 |
| East | 90 | ? | 50 | 100 | 300 |
| West | 130 | 120 | ? | 130 | 450 |
| Central | ? | 40 | 28 | 72 | 200 |
| Total | 550 | 410 | 298 | 542 | 1800 |
Answer the questions on the basis of this table.
| Region | Soaps | Shampoos | Toothpaste | Detergents | Total |
|---|---|---|---|---|---|
| North | 120 | 80 | 60 | 140 | 400 |
| South | 150 | 110 | 90 | 100 | 450 |
| East | 90 | ? | 50 | 100 | 300 |
| West | 130 | 120 | ? | 130 | 450 |
| Central | ? | 40 | 28 | 72 | 200 |
| Total | 550 | 410 | 298 | 542 | 1800 |
Answer the questions on the basis of this table.
Question 1
Numerical answer
What were the Shampoo sales (in ₹ crore) in the East region?
Show answer and solution
Answer: 60
East row: 90 + ? + 50 + 100 = 300 ⇒ ? = 60.
Cross-check with the Shampoo column: 80 + 110 + 60 + 120 + 40 = 410 ✓.
The other smudged cells: West Toothpaste = 450 − (130 + 120 + 130) = 70 and Central Soaps = 200 − (40 + 28 + 72) = 60. Completed table:
| Region | Soaps | Shampoos | Toothpaste | Detergents | Total |
|---|---|---|---|---|---|
| North | 120 | 80 | 60 | 140 | 400 |
| South | 150 | 110 | 90 | 100 | 450 |
| East | 90 | 60 | 50 | 100 | 300 |
| West | 130 | 120 | 70 | 130 | 450 |
| Central | 60 | 40 | 28 | 72 | 200 |
| Total | 550 | 410 | 298 | 542 | 1800 |
Cross-check with the Shampoo column: 80 + 110 + 60 + 120 + 40 = 410 ✓.
The other smudged cells: West Toothpaste = 450 − (130 + 120 + 130) = 70 and Central Soaps = 200 − (40 + 28 + 72) = 60. Completed table:
| Region | Soaps | Shampoos | Toothpaste | Detergents | Total |
|---|---|---|---|---|---|
| North | 120 | 80 | 60 | 140 | 400 |
| South | 150 | 110 | 90 | 100 | 450 |
| East | 90 | 60 | 50 | 100 | 300 |
| West | 130 | 120 | 70 | 130 | 450 |
| Central | 60 | 40 | 28 | 72 | 200 |
| Total | 550 | 410 | 298 | 542 | 1800 |
Question 2
Single correct option
In which region did Detergents account for the largest share of that region's total sales?
- A. North
- B. East
- C. Central
- D. West
Show answer and solution
Answer: (C) Central
Detergent share of each region's total:
- North: 140/400 = 35.0%
- South: 100/450 ≈ 22.2%
- East: 100/300 ≈ 33.3%
- West: 130/450 ≈ 28.9%
- Central: 72/200 = 36.0%
Central is highest, narrowly ahead of North. The trap is choosing North, which has the largest absolute Detergent sales (₹140 crore) but a smaller share.
Tip: When asked for 'share', always divide by the relevant row total, not the column total.
- North: 140/400 = 35.0%
- South: 100/450 ≈ 22.2%
- East: 100/300 ≈ 33.3%
- West: 130/450 ≈ 28.9%
- Central: 72/200 = 36.0%
Central is highest, narrowly ahead of North. The trap is choosing North, which has the largest absolute Detergent sales (₹140 crore) but a smaller share.
Tip: When asked for 'share', always divide by the relevant row total, not the column total.
Question 3
Numerical answer
In how many of the five regions did Detergent sales exceed Soap sales?
Show answer and solution
Answer: 3
Use the completed table (Central Soaps = 200 − 140 = 60):
- North: 140 > 120 ✓
- South: 100 < 150 ✗
- East: 100 > 90 ✓
- West: 130 = 130 ✗ (equal, not greater)
- Central: 72 > 60 ✓
Answer: 3. The West region is the trap — equal values do not count as 'exceeded'.
- North: 140 > 120 ✓
- South: 100 < 150 ✗
- East: 100 > 90 ✓
- West: 130 = 130 ✗ (equal, not greater)
- Central: 72 > 60 ✓
Answer: 3. The West region is the trap — equal values do not count as 'exceeded'.
Question 4
Single correct option
If Shampoo sales grow by 20% in every region next year while all other sales stay unchanged, the company's total sales will rise by approximately
- A. 4.6%
- B. 5.0%
- C. 4.1%
- D. 20%
Show answer and solution
Answer: (A) 4.6%
Total Shampoo sales = 410 (column total). A 20% rise adds 0.2 × 410 = ₹82 crore.
Increase in total sales = 82/1800 × 100 ≈ 4.6%.
Why not 20%? Only one of the four categories grows. A quick way: Shampoos are 410/1800 ≈ 22.8% of sales, and 20% of 22.8% ≈ 4.56%.
Increase in total sales = 82/1800 × 100 ≈ 4.6%.
Why not 20%? Only one of the four categories grows. A quick way: Shampoos are 410/1800 ≈ 22.8% of sales, and 20% of 22.8% ≈ 4.56%.
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