CAPF AC 2021 Q95: General Mental Ability – Quantitative Aptitude
- (a) 2.6% less
- (b) 2.6% more
- (c) Same price
- (d) 5.2% more
Answer: (b) 2.6% more
Explanation
Two discounts and then GST
Given: a shopkeeper gives two consecutive discounts of 10% and 5%, then adds 20% GST; the marked price is ₹2,000; find how much more or less than the marked price the customer pays.
How to think: apply each change one after another on the new price.
Percentages on changing bases must be multiplied, never added.
| Step | Working | Price |
|---|---|---|
| Marked price | Given | ₹2,000 |
| After 10% discount | 2,000 × 0.90 | ₹1,800 |
| After 5% discount | 1,800 × 0.95 | ₹1,710 |
| After 20% GST | 1,710 × 1.20 | ₹2,052 |
Compare with the marked price: 2,052 − 2,000 = ₹52 more.
52 out of 2,000 is 2.6%.
In one line: 0.90 × 0.95 × 1.20 = 1.026, which is 2.6% more.
Answer: (b) 2.6% more.
Why each option is right or wrong
- (a) Incorrect. The final price ₹2,052 is above ₹2,000, so the customer pays more, not less.
- (b) CORRECT. 0.90 × 0.95 × 1.20 = 1.026, so the customer pays 2.6% more.
- (c) Incorrect. Adding −10 − 5 + 20 = +5 is wrong, and so is assuming they cancel out.
- (d) Incorrect. 5.2% is double the true figure of 2.6%.
Key point
Successive percentage changes multiply: final = original × (1 − d1)(1 − d2)(1 + tax). Two discounts of 10% and 5% equal a single discount of 14.5%, not 15%.
Remember
Successive percentages multiply: 0.9 × 0.95 × 1.2 = 1.026.
Common mistakes
- Adding the percentages (−10 − 5 + 20 = +5%) instead of multiplying the factors.
- Treating two discounts of 10% and 5% as a single discount of 15%.
- Working out the GST on the marked price instead of the discounted price.
Exam tip
Educated guess: discounts total a bit under 15% and GST adds 20% on a smaller base, so the net result is a small increase. Only 2.6% more fits; 5.2% is too large.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (discount and sales tax or GST)
- R. S. Aggarwal, Quantitative Aptitude — Percentage and Discount