Percentage and its Applications — Multiple Choice Questions

$3\dfrac{1}{8}$% of 75 kg is equal to

1. $3\dfrac{11}{32}$ kg

2. $2\dfrac{11}{32}$ kg

3. $3\dfrac{11}{32}$ g

4. $2\dfrac{11}{32}$ g

Answer

$3\dfrac{1}{8}$% of 75 kg = $\dfrac{25}{8}$% of 75 kg

$\Rightarrow \dfrac{25}{8} \times \dfrac{1}{100} \times 75 \\[1em] \Rightarrow \dfrac{1875}{800} \\[1em] \Rightarrow \dfrac{75}{32} \\[1em] \Rightarrow 2\dfrac{11}{32}\text{ kg}$

Hence, option 2 is the correct option.

$2\dfrac{1}{12}$% is equivalent to

1. $\dfrac{3}{48}$

2. $\dfrac{5}{48}$

3. $\dfrac{1}{48}$

4. None of these

Answer

$2\dfrac{1}{12}$% = $\dfrac{25}{12}$%

$\Rightarrow \dfrac{25}{12} \times \dfrac{1}{100} \\[1em] \Rightarrow \dfrac{25}{1200} \\[1em] \Rightarrow \dfrac{1}{48}$

Hence, option 3 is the correct option.

$1\dfrac{11}{16}$ is equivalent to

1. 168.75%

2. 169.75%

3. 170.75%

4. 167.75%

Answer

$1\dfrac{11}{16} = \dfrac{27}{16}$

$\Rightarrow \dfrac{27}{16} \times 100$%

$\Rightarrow \dfrac{2700}{16}$%

⇒ 168.75%

Hence, option 1 is the correct option.

21 : 80 is equivalent to

1. 26%

2. 26.50%

3. 26.75%

4. 26.25%

Answer

21 : 80 = $\dfrac{21}{80}$

$\Rightarrow \dfrac{21}{80} \times 100$%

$\Rightarrow \dfrac{2100}{80}$%

⇒ 26.25%

Hence, option 4 is the correct option.

If 5% of a number is 42, then number is

1. 800

2. 820

3. 840

4. 860

Answer

Let the required number be $x$.

According to the given condition,

5% of $x$ = 42

$\Rightarrow \dfrac{5}{100} \times x = 42 \\[1em] \Rightarrow \dfrac{5x}{100} = 42 \\[1em] \Rightarrow x = \dfrac{42 \times 100}{5} \\[1em] \Rightarrow x = \dfrac{4200}{5} \\[1em] \Rightarrow x = 840$

Hence, option 3 is the correct option.

What % of 150 is 30?

1. 50%

2. 10%

3. 15%

4. 20%

Answer

Required percentage = $\dfrac{30}{150} \times 100$%

= $\dfrac{3000}{150}$%

= 20%

Hence, option 4 is the correct option.

A number increased by 25% gives 155. The number is

1. 132

2. 128

3. 124

4. 120

Answer

Let the required number be $x$.

New number = $\Big(1 + \dfrac{\text{Increase Percentage}}{100}\Big) \times$ Original number

Since the number is increased by 25%, we get

$\text{New number} = \Big(1 + \dfrac{25}{100}\Big)\text{ of }x \\[1em] \Rightarrow 155 = \dfrac{125}{100} \times x \\[1em] \Rightarrow x = \dfrac{155 \times 100}{125} \\[1em] \Rightarrow x = \dfrac{15500}{125} \\[1em] \Rightarrow x = 124$

Hence, option 3 is the correct option.

Naman buys a game for ₹600 and sells it for ₹750, his profit % is

1. 15%

2. 20%

3. 25%

4. 30%

Answer

C.P. of the game = ₹600

S.P. of the game = ₹750

As S.P. > C.P., there is a profit.

Profit = S.P. - C.P.

= ₹750 - ₹600

= ₹150

Profit percentage = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$%

= $\dfrac{150}{600} \times 100$%

= $\dfrac{15000}{600}$%

= 25%

Hence, option 3 is the correct option.

Cost price of a watch is ₹680. If Rishabh sells it at a profit of 35%, then S.P. is

1. ₹918

2. ₹919

3. ₹920

4. ₹921

Answer

C.P. of the watch = ₹680, profit = 35%

S.P. = $\Big(1 + \dfrac{\text{Profit Percentage}}{100}\Big) \times$ C.P.

$\text{S.P. of the watch} = \Big(1 + \dfrac{35}{100}\Big)\text{ of C.P.} \\[1em] = \dfrac{135}{100} \times 680 \\[1em] = \dfrac{91800}{100} \\[1em] = ₹918$

Hence, option 1 is the correct option.

On selling an article for ₹150, Riya gains ₹30. Her gain percentage is

1. 15%

2. 20%

3. 25%

4. 30%

Answer

S.P. of the article = ₹150

Gain = ₹30

C.P. of the article = S.P. - Gain

= ₹150 - ₹30

= ₹120

Gain percentage = $\dfrac{\text{Gain}}{\text{C.P.}} \times 100$%

= $\dfrac{30}{120} \times 100$%

= $\dfrac{3000}{120}$%

= 25%

Hence, option 3 is the correct option.

If the cost price of 5 articles is equal to the selling price of 6 articles, then there is

1. gain

2. loss

3. no gain no loss

4. none of these

Answer

Let the cost price of one article be ₹$x$.

C.P. of 5 articles = ₹$5x$

It is given that S.P. of 6 articles = C.P. of 5 articles

∴ S.P. of 6 articles = ₹$5x$

∴ S.P. of one article = ₹$\dfrac{5x}{6}$

As $\dfrac{5x}{6} \lt x$, the selling price of one article is less than its cost price.

Therefore, there is a loss.

Hence, option 2 is the correct option.

Marked price of an article is ₹675. If it is sold at a discount of 20%, then S.P. is

1. ₹540

2. ₹525

3. ₹510

4. ₹500

Answer

M.P. of the article = ₹675, discount = 20%

S.P. = $\Big(1 - \dfrac{\text{Discount Percentage}}{100}\Big) \times$ M.P.

$\text{S.P. of the article} = \Big(1 - \dfrac{20}{100}\Big)\text{ of M.P.} \\[1em] = \dfrac{80}{100} \times 675 \\[1em] = \dfrac{54000}{100} \\[1em] = ₹540$

Hence, option 1 is the correct option.

A jacket is marked for ₹2,590. If the S.P. of jacket is ₹2,331, then discount % is

1. 5%

2. 10%

3. 15%

4. 20%

Answer

M.P. of the jacket = ₹2,590

S.P. of the jacket = ₹2,331

Discount = M.P. - S.P.

= ₹2,590 - ₹2,331

= ₹259

Discount percentage = $\dfrac{\text{Discount}}{\text{M.P.}} \times 100$%

= $\dfrac{259}{2590} \times 100$%

= $\dfrac{25900}{2590}$%

= 10%

Hence, option 2 is the correct option.

Marked price of a showpiece is ₹950. S.P. of showpiece after two successive discounts of 10% and 10% is

1. ₹769.50

2. ₹760

3. ₹855

4. None of these.

Answer

M.P. of the showpiece = ₹950

Two successive discounts = 10% and 10%

S.P. = $\Big(1 - \dfrac{d_1}{100}\Big)\Big(1 - \dfrac{d_2}{100}\Big) \times$ M.P., where $d_1$% and $d_2$% are the two successive discounts.

$\text{S.P. of the showpiece} = \Big(1 - \dfrac{10}{100}\Big)\Big(1 - \dfrac{10}{100}\Big)\text{ of M.P.} \\[1em] = \dfrac{90}{100} \times \dfrac{90}{100} \times 950 \\[1em] = \dfrac{9}{10} \times \dfrac{9}{10} \times 950 \\[1em] = \dfrac{76950}{100} \\[1em] = ₹769.50$

Hence, option 1 is the correct option.

S.P. of a board game is ₹784 including 12% GST. The original price of board game is

1. ₹801.43

2. ₹742

3. ₹700

4. None of these.

Answer

S.P. of the board game = ₹784 including 12% GST

Let the original price of the board game be ₹$x$.

GST = 12% of ₹$x$ = ₹$\dfrac{12x}{100}$

S.P. = Original price + GST

$\Rightarrow 784 = x + \dfrac{12x}{100} \\[1em] \Rightarrow 784 = \dfrac{100x + 12x}{100} \\[1em] \Rightarrow 784 = \dfrac{112x}{100} \\[1em] \Rightarrow x = \dfrac{784 \times 100}{112} \\[1em] \Rightarrow x = \dfrac{78400}{112} \\[1em] \Rightarrow x = 700$

Hence, option 3 is the correct option.

List price of an article is ₹1,050. If 18% GST is charged, then bill amount is

1. ₹1,068

2. ₹1,239

3. ₹1,131

4. ₹1,311

Answer

List price of the article = ₹1,050

Rate of GST = 18%

GST = 18% of ₹1,050

$= \dfrac{18}{100} \times 1050 \\[1em] = \dfrac{18900}{100} \\[1em] = ₹189$

Bill amount = List price + GST

= ₹1,050 + ₹189

= ₹1,239

Hence, option 2 is the correct option.