A shop sells three items: X, Y, Z. In January, X sold 100 units at Rs. 50/unit, Y sold 80 units at Rs. 60/unit, Z sold 50 units at Rs. 40/unit. In February, X’s units increased by 20%, Y’s by 25%, Z’s by 10%. Prices remain the same.
- Step 1: Calculate February units.
Apply the stated percentage increases to January units: X = 100 × 1.20 = 120;
Y = 80 × 1.25 = 100;
Z = 50 × 1.10 = 55.
- Step 2: Calculate revenue (units × price).
X: 120 × 50 = 6,000;
Y: 100 × 60 = 6,000;
Z: 55 × 40 = 2,200.
- Step 3: Total February revenue.
6,000 + 6,000 + 2,200 = 14,200.
- Step 4: Verify (percent method cross-check).
Increases: X adds 20 units (100 × 20%) so 100 + 20 = 120;
Y adds 20 units (80 × 25%)
so 80 + 20 = 100;
Z adds 5 units (50 × 10%)
so 50 + 5 = 55.
Revenues recomputed: 120 × 50 = 6,000;
100 × 60 = 6,000;
55 × 40 = 2,200;
total still 14,200.
- Step 5: Check options.
Compare the computed total (14,200) with the given choices.
The value 14,200 corresponds to Option (3).
- Step 6: Conclusion. February’s total revenue is Rs. 14,200; therefore, Option (3)
- Step 1: Find revenues. From earlier questions, January revenue (from Q25) is Rs. 11,800. February revenue (from Q26, adjusted) is Rs. 14,300. These are the starting figures for our calculation.
- Step 2: Calculate increase. Increase in revenue = February revenue − January revenue = 14,300 − 11,800 = Rs. 2,500. This tells us the absolute growth in revenue over the period.
- Step 3: Calculate percentage increase. Percentage increase formula = (Increase ÷ January revenue) × 100. Substituting values: (2,500 ÷ 11,800) × 100.
• First, divide: 2,500 ÷ 11,800 ≈ 0.211864.
• Then, multiply by 100: 0.211864 × 100 ≈ 21.1864%.
• Round to two decimal places: ≈ 21.19%.
- Step 4: Verify calculation. Quick check: 2,500 ÷ 11,800 ≈ 0.2119, multiplying by 100 again gives ≈ 21.19%, confirming accuracy.
- Step 5: Match with given options. Options: (1) 20.34%, (2) 21.19%, (3) 22.03%, (4) 23.88%. Our computed percentage (21.19%) exactly matches option (2).
- Step 6: Conclusion. The percentage increase in revenue from January to February is 21.19%, therefore the correct answer is Option (2).
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