Percentage Questions and Answers

Answer: B

Manish throws away 23 per cent of his mangoes.

Start with 100 mangoes and follow them through both days:

\[ \begin{aligned} \text{after selling 60\%} &: 40\ \text{left} \\ \text{thrown on day 1} &= 15\% \times 40 = 6 \\ \text{left} &= 34 \\ \text{sold on day 2} &= 50\% \times 34 = 17 \\ \text{thrown on day 2} &= 17 \end{aligned} \]

In total he throws away \(6 + 17 = 23\) of every 100 mangoes. A common slip is to take 15% of the original 100 instead of the 40 left, which gives 15 thrown on the first day and a different total; since 23 is offered, 'None of these' is wrong.

Answer: D

The smaller number is \(16\frac{2}{3}\)% of the sum.

Let the numbers be x and y. Since 12.5% of x equals 62.5% of y, x = 5y. Then use the sum of squares:

\[ \begin{aligned} (5y)^{2} + y^{2} &= 416 \\ 26y^{2} &= 416 \\ y^{2} = 16, \ y &= 4, \ x = 20 \end{aligned} \]

The smaller number is 4 and the sum is 24:

\[ \frac{4}{24} \times 100 = 16\tfrac{2}{3}\% \]

\(83\frac{1}{3}\)% is the larger number's share (20 out of 24), and 20% and 25% compare the smaller number with the larger (4/20) or use a wrong ratio, not with the sum.

Answer: D

\[ 0.30A + 0.40B = 0.80B \]

\[ 0.30A = 0.40B \quad\Longrightarrow\quad \frac{B}{A} = \frac{0.30}{0.40} = 0.75 \]

So B is 75% of A. Note the question asks for B as a percentage of A, not the other way round - that would be 133.3%.

Answer: D

Total income of man = Rs. \(100x\)

Amount spend \(= \frac{59}{100} \times 100x = 59x\) (Rs.)

\(\Rightarrow \) Money saved \(= 100x - 59x = 41x\)

\(\therefore\) Percentage of his expenditure that he saves \(= \frac{41x}{59x} \times 100 = 69.49 \) %

Answer: B

The retailer buys 110 gram in Rs 100 because of 10 % cheating so cost price = 1 gram = Rs \(\frac{100}{110}\) = Rs 0.909 and retailer sells 90 gram in Rs 100

and hence selling price = Rs 100 / 90 = Rs 1.111

Profit % \(= \frac{1.111-0.909}{0.909} = 22.22\)

Answer: B

Train ticket cost for 1 day = Rs. 130

⇒ Cost for 29 days \(= 29 \times \times 130 = Rs.3770\)

Cost of monthly pass = Rs. 3091.40

⇒ Money saved = 3770 - 3091.40 = Rs. 678.6

\(\therefore\) Required % \(= \frac{678.6}{3770} \times 100 = 18\)

Answer: A

 The number of boys be 2y and number of girls be 3y

25 % of boys \(= 0.25 \times 2y = 0.5y\)

30 % of girls \(= 0.3 \times 3y = 0.9y\)

total scholarship holder \(= 0.5y +0.9y = 1.4y\)

% of no scholership holder \(= \frac{3.6y}{5y} \times 100 = 72\)

Answer: D

Let the length of rectangle be \(L\) units and breadth be \(B\) units.

So area of rectangle \(= L \times B\)

As both length and breadth has been increased by 20%

So new length = 1.2\(L\)

New breadth = 1.2\(B\)

New area \(= 1.2L \times 1.2B = 1.44LB\)

Percentage increase in area \(= \frac{1.44LB-LB}{LB} \times 100 = 44\)

Answer: C

The income of person be Rs \(y\)

So his expenditure be 75% of income which is \(= 0.75y\)

Saving \(= y- 0.75y = 0.25​​​​​​​y\)

Now after increment of 20 % in income the new income becomes \(= 1.2y\)

Given that bew expenditure is 10% more than previous one.So , new expenditure is \(= 1.1 \times 0.75y = 0.825y\)

New savings \(= 1.2y - 0.825y = 0.375y\)

Percentage increase in savings \(= \frac{0.375y-0.25y}{0.25y} \times 100 = 50%\)

Answer: C

Marked price \(= Rs. 1280\)

Selling price \(= Rs. 900\)

⇒ Discount % \(= \frac{1280-900}{1280} \times 100 \)

\(= \frac{380}{12.8} \)

\(= 29.68\)