Arithmetic Applications (Level 1): MCQ test, Set 3

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Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

Find the ratio of the price of coffee to that of tea, when coffee costs ₹45 per 100 g and tea costs ₹600 per kg.
A $15 : 2$ B $3 : 4$ C $3 : 40$ D $4 : 3$

Answer and solution

Answer: (B) $3 : 4$

100 g of coffee costs ₹45, so 1000 g (1 kg) costs ₹450.

$\displaystyle \text{Required ratio} = \frac{450}{600} = \frac{3}{4} = 3 : 4$
If ₹1440 is divided into two parts in the ratio $7 : 9$ , then the smaller part is
A ₹90 B ₹630 C ₹180 D ₹810

Answer and solution

Answer: (B) ₹630

$\displaystyle \text{Smaller part} = \frac{7}{7 + 9} \times 1440 = \frac{7}{16} \times 1440 = 630$
The ratio of boys to girls in a school with 720 students is $7 : 5$ . If 30 more girls are admitted, the new ratio of boys to girls is
A $7 : 6$ B $7 : 5$ C $3 : 2$ D $14 : 11$

Answer and solution

Answer: (D) $14 : 11$

$\displaystyle \text{Boys} = \frac{7}{12} \times 720 = 420, \quad \text{Girls} = 720 - 420 = 300$

$\displaystyle \text{New ratio} = \frac{420}{330} = 14 : 11$
In the proportion $3 : 5 :: 12 : 20$ , the means are
A $3$ and $20$ B $12$ and $20$ C $5$ and $12$ D $3$ and $5$

Answer and solution

Answer: (C) $5$ and $12$

In $a : b :: c : d$ , the second and third terms are the means.

So the means are $5$ and $12$ (and $5 \times 12 = 60 = 3 \times 20$ ).
If 16, $x$ , $x$ , 25 are in proportion, then $x =$
A $400$ B $20.5$ C $20$ D $9$

Answer and solution

Answer: (C) $20$

$\displaystyle \frac{16}{x} = \frac{x}{25} \Rightarrow x^2 = 400 \Rightarrow x = 20$
If $a : b = c : d$ , then $\displaystyle \frac{a+b}{a-b} = \frac{c+d}{c-d}$ . This property is called
A Dividendo B Componendo C Addendo D Componendo and dividendo

Answer and solution

Answer: (D) Componendo and dividendo

Adding (componendo) and subtracting (dividendo) together gives $\displaystyle \frac{a+b}{a-b} = \frac{c+d}{c-d}$ : componendo and dividendo.
The cost of 8 m of cloth is ₹456. The cost of 5 m of the same cloth is (in ₹)
A $285$ B $57$ C $729.6$ D $342$

Answer and solution

Answer: (A) $285$

Direct proportion: $x_1 y_2 = x_2 y_1$

$\displaystyle y = \frac{5 \times 456}{8} = 285$
12 pumps fill a tank in 45 minutes. If 3 pumps go out of order, the remaining pumps fill it in
A $48$ minutes B $60$ minutes C $33.75$ minutes D $54$ minutes

Answer and solution

Answer: (B) $60$ minutes

Inverse proportion: $x_1 y_1 = x_2 y_2$

$12 \times 45 = 9 \times y \Rightarrow y = 60$
$0.07$ expressed as a percentage is
A $0.07\%$ B $0.7\%$ C $7\%$ D $70\%$

Answer and solution

Answer: (C) $7\%$

$0.07 = (0.07 \times 100)\% = 7\%$
What percent of 6 is 9?
A $\displaystyle 66\frac{2}{3}\%$ B $150\%$ C $54\%$ D $15\%$

Answer and solution

Answer: (B) $150\%$

$\displaystyle \left(\frac{9}{6} \times 100\right)\% = 150\%$
By what percent is 72 more than 60?
A $20\%$ B $\displaystyle 16\frac{2}{3}\%$ C $120\%$ D $12\%$

Answer and solution

Answer: (A) $20\%$

Change $= 12$

$\displaystyle \left(\frac{12}{60} \times 100\right)\% = 20\%$

Always divide by the original value.
The price of tea rises by $20\%$ . To keep the expenditure the same, consumption must be reduced by
A $20\%$ B $25\%$ C $10\%$ D $\displaystyle 16\frac{2}{3}\%$

Answer and solution

Answer: (D) $\displaystyle 16\frac{2}{3}\%$

$\displaystyle \left(\frac{20}{100 + 20} \times 100\right)\% = \left(\frac{20}{120} \times 100\right)\% = 16\frac{2}{3}\%$
A population of 10000 increases at $10\%$ per annum. After 3 years it will be
A $13{,}310$ B $12{,}100$ C $13{,}000$ D $14{,}641$

Answer and solution

Answer: (A) $13{,}310$

$\displaystyle 10000\left(\frac{11}{10}\right)^3 = 13310$
An agent gets $2\%$ commission on his sales. If his commission is ₹350, the goods sold are worth
A ₹1,75,000 B ₹7000 C ₹1750 D ₹17,500

Answer and solution

Answer: (D) ₹17,500

$\displaystyle \frac{2}{100}x = 350 \Rightarrow x = \frac{350 \times 100}{2} = 17500$
The cost price of an article is ₹480 and the markup is $35\%$ . Its marked price is
A ₹648 B ₹312 C ₹515 D ₹168

Answer and solution

Answer: (A) ₹648

$\displaystyle \text{M.P} = 480 + \frac{35}{100} \times 480 = 480 + 168 = 648$
Two chairs are sold at ₹1500 each, one at $25\%$ profit and the other at $25\%$ loss. On the whole there is a
A loss of $2.5\%$ B neither profit nor loss C loss of $6.25\%$ D gain of $6.25\%$

Answer and solution

Answer: (C) loss of $6.25\%$

Same S.P, $a\%$ profit and $a\%$ loss: always a loss of $\displaystyle \left(\frac{a}{10}\right)^2\%$ .

$\displaystyle \left(\frac{25}{10}\right)^2 = 6.25\%$
If the cost price of 24 articles equals the selling price of 18 articles, then there is a
A $25\%$ loss B $\displaystyle 33\frac{1}{3}\%$ loss C $\displaystyle 33\frac{1}{3}\%$ gain D $25\%$ gain

Answer and solution

Answer: (C) $\displaystyle 33\frac{1}{3}\%$ gain

$\displaystyle 24x = 18y \Rightarrow \frac{y}{x} = \frac{4}{3}$

$\displaystyle \left(\frac{y}{x} - 1\right) \times 100 = 33\frac{1}{3}\%$ (a gain)
The average of 9 numbers is 42. The average of the first 4 is 40 and that of the last 4 is 45. The 5th number is
A $42$ B $38$ C $45$ D $40$

Answer and solution

Answer: (B) $38$

Sum of 9 $= 378$ , first 4 $= 160$ , last 4 $= 180$

$x_5 = 378 - 160 - 180 = 38$
The average of $x_1, x_2, \ldots, x_n$ is 12. The average of $2x_1 + 5, 2x_2 + 5, \ldots, 2x_n + 5$ is
A $24$ B $17$ C $34$ D $29$

Answer and solution

Answer: (D) $29$

Average of $ax_i + b$ is $a\bar{x} + b = 2(12) + 5 = 29$
If a man travels at 40 km/h, he reaches his destination 12 minutes late, and at 60 km/h he reaches 8 minutes early. The distance travelled is
A $40$ km B $30$ km C $36$ km D $48$ km

Answer and solution

Answer: (A) $40$ km

Let $T$ be the correct time (hours): $\displaystyle D = 40\left(T + \frac{12}{60}\right) = 60\left(T - \frac{8}{60}\right)$

$\displaystyle \Rightarrow T = \frac{4}{5} \text{ h}, \quad D = 40 \times 1 = 40 \text{ km}$
A cyclist covers three equal distances at 20 km/h, 30 km/h and 60 km/h. His average speed is
A $30$ km/h B $\displaystyle 36\frac{2}{3}$ km/h C $36$ km/h D $25$ km/h

Answer and solution

Answer: (A) $30$ km/h

$\displaystyle \frac{3 \times 20 \times 30 \times 60}{600 + 1800 + 1200} = \frac{1{,}08{,}000}{3600} = 30$
The speeds of two trains are in the ratio $4 : 5$ . The first takes 10 hours for a journey. The second takes
A $9$ hours B $11$ hours C $8$ hours D $12.5$ hours

Answer and solution

Answer: (C) $8$ hours

$s_1 : s_2 = T_2 : T_1 \Rightarrow 4 : 5 = T_2 : 10$

$\displaystyle T_2 = \frac{4 \times 10}{5} = 8$ hours
Two trains are moving in the same direction at 68 km/h and 50 km/h. Their relative speed is
A $118$ km/h B $18$ km/h C $34$ km/h D $59$ km/h

Answer and solution

Answer: (B) $18$ km/h

Same direction: relative speed $= (x - y) = 68 - 50 = 18$ km/h
The simple interest on ₹1250 for 4 years is ₹300. The rate of interest per annum is
A $24\%$ B $1.5\%$ C $8\%$ D $6\%$

Answer and solution

Answer: (D) $6\%$

$\displaystyle R = \frac{300 \times 100}{1250 \times 4} = 6\%$
The amount on ₹8000 at $10\%$ per annum for 1 year, compounded half-yearly, is
A ₹8400 B ₹8800 C ₹9680 D ₹8820

Answer and solution

Answer: (D) ₹8820

$k = 2$ : $\displaystyle A = 8000\left(1 + \frac{10}{200}\right)^2 = 8000 \times \frac{21}{20} \times \frac{21}{20} = 8820$

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MCQ test, Set 3