Arithmetic Applications (Level 1): MCQ test, Set 6

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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.

In the ratio $13 : 20$ , the consequent (second term) is
A $20$ B $33$ C $\displaystyle \frac{13}{20}$ D $13$

Answer and solution

Answer: (A) $20$

In $a : b$ , $a$ is the antecedent and $b$ is the consequent.

So the consequent of $13 : 20$ is $20$ .
₹3900 is divided among three persons in the ratio $2 : 4 : 7$ . The first share is
A ₹300 B ₹600 C ₹1200 D ₹2100

Answer and solution

Answer: (B) ₹600

Sum of the terms $= 2 + 4 + 7 = 13$

$\displaystyle \text{First share} = \frac{2}{13} \times 3900 = 600$
If $\displaystyle 2\frac{1}{4} : 1\frac{2}{3} : 2\frac{1}{2}$ is $A : B : C$ , then
A $A > B > C$ B $A > C > B$ C $C > A > B$ D $B > A > C$

Answer and solution

Answer: (C) $C > A > B$

$\displaystyle A : B : C = \frac{9}{4} : \frac{5}{3} : \frac{5}{2}$

L.C.M of the denominators $= 12$

$\displaystyle = \frac{27}{12} : \frac{20}{12} : \frac{30}{12} = 27 : 20 : 30$

$\therefore C > A > B$
If $7 : x :: 28 : 36$ , then $x =$
A $144$ B $9$ C $\displaystyle 5\frac{4}{9}$ D $252$

Answer and solution

Answer: (B) $9$

Product of means $=$ product of extremes.

$28x = 7 \times 36 \Rightarrow x = 9$
The third proportional to 8 and 20 is
A $3.2$ B $4\sqrt{10}$ C $160$ D $50$

Answer and solution

Answer: (D) $50$

$8 : 20 :: 20 : c \Rightarrow 8c = 20 \times 20$

$\displaystyle c = \frac{400}{8} = 50$
If $\displaystyle \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{3}{4}$ , then $\displaystyle \frac{a + 2c + 5e}{b + 2d + 5f} =$
A $\displaystyle \frac{3}{4}$ B $\displaystyle \frac{3}{32}$ C $\displaystyle \frac{4}{3}$ D $6$

Answer and solution

Answer: (A) $\displaystyle \frac{3}{4}$

If $\displaystyle \frac{a}{b} = \frac{c}{d} = \frac{e}{f}$ then each equals $\displaystyle \frac{ap + cq + er}{bp + dq + fr}$ .

Here $p = 1$ , $q = 2$ , $r = 5$ , so the value is $\displaystyle \frac{3}{4}$ .
If 7 chairs cost ₹5810, then 4 such chairs cost (in ₹)
A $4150$ B $830$ C $3320$ D $10167.5$

Answer and solution

Answer: (C) $3320$

Direct proportion: $x_1 y_2 = x_2 y_1$

$\displaystyle y = \frac{4 \times 5810}{7} = 3320$
In a fort there is food for 800 men for 30 days. Some men left and the food lasted for 40 days. The number of men who left is
A $600$ B $200$ C $100$ D $300$

Answer and solution

Answer: (B) $200$

$800 \times 30 = (800 - x) \times 40$

$800 - x = 600 \Rightarrow x = 200$
$\displaystyle 1\frac{1}{4}$ expressed as a percentage is
A $125\%$ B $1.25\%$ C $25\%$ D $12.5\%$

Answer and solution

Answer: (A) $125\%$

$\displaystyle 1\frac{1}{4} = \frac{5}{4} = \left(\frac{5}{4} \times 100\right)\% = 125\%$
$8\%$ of 650 is
A $5.2$ B $520$ C $52$ D $81.25$

Answer and solution

Answer: (C) $52$

$\displaystyle \frac{8}{100} \times 650 = 52$
The price of a fan falls from ₹750 to ₹600. The percentage decrease is
A $15\%$ B $25\%$ C $80\%$ D $20\%$

Answer and solution

Answer: (D) $20\%$

Change $= 150$

$\displaystyle \left(\frac{150}{750} \times 100\right)\% = 20\%$

Always divide by the original value.
If $A$ is $40\%$ less than $B$ , then $B$ is more than $A$ by
A $40\%$ B $\displaystyle 66\frac{2}{3}\%$ C $60\%$ D $\displaystyle 28\frac{4}{7}\%$

Answer and solution

Answer: (B) $\displaystyle 66\frac{2}{3}\%$

$\displaystyle \left(\frac{40}{100 - 40} \times 100\right)\% = \left(\frac{40}{60} \times 100\right)\% = 66\frac{2}{3}\%$
A town has 5000 people. If the population grows at $8\%$ per annum, after 2 years it will be
A $6000$ B $5400$ C $5800$ D $5832$

Answer and solution

Answer: (D) $5832$

$\displaystyle 5000\left(\frac{27}{25}\right)^2 = 5832$
By selling 36 bags, a vendor loses the selling price of 9 bags. His loss percent is
A $25\%$ B $\displaystyle 33\frac{1}{3}\%$ C $9\%$ D $20\%$

Answer and solution

Answer: (D) $20\%$

S.P of 36 bags $= 36$ (taking ₹1 each), Loss $= 9$ , C.P $= 45$

Loss $\displaystyle \% = \frac{9}{45} \times 100 = 20\%$
A man got a $30\%$ concession on the label price of a watch. He sold it for ₹6300 at a $20\%$ profit on his price. The label price was
A ₹9000 B ₹7500 C ₹8190 D ₹5250

Answer and solution

Answer: (B) ₹7500

C.P $\displaystyle = \frac{70}{100}x$ ; S.P $\displaystyle = \frac{120}{100} \times \frac{70}{100}x = 6300$

$\displaystyle x = \frac{6300 \times 10000}{120 \times 70} = 7500$
A trader claims to sell milk at cost price but gives only 750 ml for every litre. His gain percent is
A $\displaystyle 33\frac{1}{3}\%$ B $\displaystyle 133\frac{1}{3}\%$ C $75\%$ D $25\%$

Answer and solution

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

Gain $\displaystyle \% = \frac{\text{Error}}{\text{True value} - \text{Error}} \times 100$

$\displaystyle = \frac{250}{750} \times 100 = 33\frac{1}{3}\%$
A shopkeeper buys lemons at 7 for ₹10 and sells them at 5 for ₹8. His profit percent is
A $-12\%$ B $25\%$ C $12\%$ D $\displaystyle 10\frac{5}{7}\%$

Answer and solution

Answer: (C) $12\%$

$\displaystyle \text{C.P} \text{ of one} = \frac{10}{7}, \quad \text{S.P} \text{ of one} = \frac{8}{5}$

$\displaystyle \text{Profit \%} = \frac{\frac{8}{5} - \frac{10}{7}}{\frac{10}{7}} \times 100 = 12\%$
In the first 20 overs of a 50-over cricket match, the run rate was 4.5. The run rate needed in the remaining 30 overs to reach a target of 300 runs is
A $4.2$ B $7$ C $10$ D $6$

Answer and solution

Answer: (B) $7$

Runs in 20 overs $= 4.5 \times 20 = 90$ ; needed $= 300 - 90 = 210$

Run rate $\displaystyle = \frac{210}{30} = 7$
The average weight of 12 men increases by 2 kg when a new man replaces one weighing 64 kg. The weight of the new man (in kg) is
A $88$ B $40$ C $90$ D $66$

Answer and solution

Answer: (A) $88$

$N = 64 + 12 \times 2 = 64 + 24 = 88$ kg
A bus travelling at 40 km/h covers one-fifth of the distance between two towns in 2 hours. The distance between the towns (in km) is
A $200$ B $80$ C $400$ D $16$

Answer and solution

Answer: (C) $400$

In 2 h it covers $40 \times 2 = 80$ km $\displaystyle = \frac{x}{5}$

$x = 80 \times 5 = 400$ km
If a car travels from $A$ to $B$ at $a$ km/h and from $B$ to $A$ at $b$ km/h, its average speed is
A $\displaystyle \frac{a + b}{2}$ B $\displaystyle \frac{ab}{a + b}$ C $\displaystyle \frac{2(a + b)}{ab}$ D $\displaystyle \frac{2ab}{a + b}$

Answer and solution

Answer: (D) $\displaystyle \frac{2ab}{a + b}$

$\displaystyle \frac{d + d}{\frac{d}{a} + \frac{d}{b}} = \frac{2}{\frac{1}{a} + \frac{1}{b}} = \frac{2ab}{a + b}$
A bus takes $\displaystyle \frac{3}{4}$ of the time a car takes for the same journey. If the car's speed is 60 km/h, the bus's speed is
A $75$ km/h B $80$ km/h C $70$ km/h D $45$ km/h

Answer and solution

Answer: (B) $80$ km/h

$s_{bus} : s_{car} = T_{car} : T_{bus} = 4 : 3$

Bus speed $\displaystyle = 60 \times \frac{4}{3} = 80$ km/h
A train 225 m long running at 54 km/h passes a telegraph pole in
A $15$ seconds B $\displaystyle 4\frac{1}{6}$ seconds C $30$ seconds D $54$ seconds

Answer and solution

Answer: (A) $15$ seconds

Speed $\displaystyle = 54 \times \frac{5}{18} = 15$ m/s

$\displaystyle T = \frac{225}{15} = 15$ s
The simple interest on ₹1200 at $9\%$ per annum for 8 months is
A ₹108 B ₹96 C ₹864 D ₹72

Answer and solution

Answer: (D) ₹72

$\displaystyle T = \frac{8}{12} = \frac{2}{3}$ year

$\displaystyle \text{S.I} = \frac{1200 \times 2 \times 9}{3 \times 100} = 72$
The bacteria count in a sample is 20000. It increases by $10\%$ in the first hour, decreases by $20\%$ in the second and increases by $10\%$ in the third. The count after 3 hours is
A $18{,}000$ B $29{,}040$ C $19{,}360$ D $20{,}000$

Answer and solution

Answer: (C) $19{,}360$

$\displaystyle 20000 \times \frac{110}{100} \times \frac{80}{100} \times \frac{110}{100} = 19360$

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MCQ test, Set 6