Percentage Questions and Answers

Answer: D

The savings are 20% of A, 15% of B and 25% of C, and they are in the ratio 7 : 6 : 9. Let the savings be 7k, 6k and 9k. Then:

The total salary 111k = Rs 33,300 gives k = 300, so B = 40 x 300 = Rs 12,000, option D.

Check: A earns 10,500, B earns 12,000 and C earns 10,800, which sum to 33,300, and the savings 2,100, 1,800 and 2,700 are in the ratio 7 : 6 : 9.

Answer: D

The original price is Rs. 30 per kg.

Let the original price be \(p\). After a 10% cut the price is \(0.9p\), and Rs. 270 buys 1 kg more:

\[ \begin{aligned} \frac{270}{0.9p} - \frac{270}{p} &= 1 \\ \frac{300 - 270}{p} &= 1, \quad p = 30 \end{aligned} \]

Check: at Rs. 30, Rs. 270 buys 9 kg; at Rs. 27 it buys 10 kg. Rs. 27 is the reduced price, the usual trap.

Answer: C

The maximum marks are 150.

Y scored 20 marks and fell 40 marks short, so the pass mark is \(20 + 40 = 60\). The pass mark is 40% of the maximum:

\[ \begin{aligned} 0.4 \times M &= 60 \\ M &= \frac{60}{0.4} = 150 \end{aligned} \]

Check: 40% of 150 is 60, and 60 minus his 20 is the 40 marks he missed by. 100 would make the pass mark only 40, and 200 or 250 would make it 80 or 100, so he would have failed by 60 or 80 marks instead.

Answer: A

His total income is Rs. 7500.00.

Let the income be \(x\). Rent takes 20%, leaving \(0.8x\). Household spending is 70% of that rest, so he saves the other 30% of it.

\[ \begin{aligned} \text{savings} &= 0.3 \times 0.8x = 0.24x \\ 0.24x &= 1800 \\ x &= 7500 \end{aligned} \]

Check: rent is Rs. 1500, leaving Rs. 6000; household spending is 70% of 6000, Rs. 4200; savings are \(6000 - 4200 = 1800\). Taking 70% of the whole income instead of the rest leaves savings of 10%, giving Rs. 18000, which is why 'None of these' tempts; Rs. 8500 and Rs. 7200 do not give savings of Rs. 1800.

Answer: A

B's salary is 20% less than A's.

Take B's salary as 100. Then A's is 25% more, 125. The difference is 25, but it must now be compared with A's salary, the new base:

\[ \frac{25}{125} \times 100 = 20\% \]

The general rule: if A is \(r\%\) more than B, then B is \(\frac{r}{100 + r} \times 100\%\) less than A. 25% is the trap of reusing the same percentage with the wrong base; 30% and 15% match no step of the working.

Answer: C

The equivalent single discount is 28%.

Successive discounts multiply, they do not add. On a marked price of 100:

\[ \begin{aligned} \text{after } 10\% &: 100 \times 0.9 = 90 \\ \text{after } 20\% &: 90 \times 0.8 = 72 \\ \text{discount} &= 100 - 72 = 28\% \end{aligned} \]

Shortcut: for discounts \(a\%\) and \(b\%\), the single discount is \(a + b - \frac{ab}{100} = 10 + 20 - 2 = 28\%\). Adding them gives 30%, which is not offered; 24%, 15% and 32% match no correct working.

Answer: C

The number is 600.

If 15% of the number is 90, then:

\[ \begin{aligned} \frac{15}{100} \times x &= 90 \\ x &= \frac{90 \times 100}{15} = 600 \end{aligned} \]

Check: 10% of 600 is 60 and 5% is 30, which make 90. 500 gives 75, 550 gives 82.5 and 650 gives 97.5, so none of them has 90 as its 15%.

Answer: A

The maximum marks are 720.

The pass mark is what the student scored plus the shortfall, and it equals 40% of the maximum:

\[ \begin{aligned} \text{pass mark} &= 250 + 38 = 288 \\ 0.4 \times M &= 288 \\ M &= 720 \end{aligned} \]

Check: 40% of 720 is 288. 760, 820 and 850 would need pass marks of 304, 328 and 340, so a student with 250 would fail by more than 38 marks.

Answer: C

The smallest such whole number is 8.

We need 40% of the number to exceed 3:

\[ \begin{aligned} 0.4n &> 3 \\ n &> 7.5 \end{aligned} \]

The smallest whole number greater than 7.5 is 8, and 40% of 8 is 3.2, which is more than 3. 40% of 7 is only 2.8 and 40% of 6 is 2.4, both less than 3, so they fail. 9 also works (40% of 9 is 3.6), but it is not the smallest such number, which is what the question asks for.

Answer: A

His present salary is 64% of the original.

Successive percentage changes multiply. Taking the initial salary as 100:

\[ \begin{aligned} 100 \times 0.4 &= 40 \\ 40 \times 1.6 &= 64 \end{aligned} \]

The trap is to think a 60% fall and a 60% rise cancel out. They do not, because the rise is 60% of the smaller, reduced salary. 60%, 62% and 68% do not come from this calculation.