Comparing Quantities Test

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Comparing Quantities Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

A invested Rs 76000 in a business After few months B joined him with Rs 57000 At the end of the year the total profit was divided between them in the ratio of 2 :1 After how many months did B join?

A
4

B
8

C
9

D
None of these

Solution

Let A invested Rs.76000 for 12 months and B invested Rs.57000 for x months
Then $$\frac{7600\times 12}{5700\times x}=\frac{2}{1}$$
$$\Rightarrow x=\frac{76\times 12}{57\times 2}$$
$$\Rightarrow x=8$$
hence B invested for 8 months
Question 2
1 / -0

A, B and C enter into a partnership They invest Rs 40000, Rs 80000 and Rs 120000 respectively At the end of the first year B withdraws Rs 40000 while at the end of the second year C withdraws Rs 80000 In what ratio will the profit be shared at the end of 3 years?

A
2 : 3 : 5

B
3 : 4 : 7

C
4 : 5 : 9

D
None of these

Solution

$$A:B:C=(40000\times 36):(80000\times 12+40000\times 24):(120000\times 24+40000\times 12)$$
$$\Rightarrow 1440000:1920000:3360000$$
$$\Rightarrow 144:192:336$$
$$\Rightarrow 12:16:28$$
$$\Rightarrow 3:4:7$$
Question 3
1 / -0

A and B entered into partnership with capitals in the ratio 4 : 5 After 3 months A withdraw $$\displaystyle \frac{1}{4}$$ of his capital and B withdraw $$\displaystyle \frac{1}{5}$$ of his capital. The gain at the end of 10 months was Rs 760. A's share in this profit is

A
Rs 330

B
Rs 360

C
Rs 380

D
Rs 430

Solution

Ratio of the initial capital of A and B = 4 : 5
Hence the initial capitals of A and B is 4x and 5x
Ratio in which profit will be divided
$$(4x\times 3)+(\frac{3}{4}\times 4x\times 7):(5x\times 3)+(\frac{4}{5}\times 5x\times 7)$$
$$33:43$$
A's share=$$\frac{33}{76}\times 760=Rs 330$$
Question 4
1 / -0

Rakesh took a loan for $$7$$ years at the rate of $$6\%$$ p.a. $$S.I$$. If the total interest paid was Rs. $$2100$$, the principal was

A
Rs. $$4400$$

B
Rs. $$4800$$

C
Rs. $$5000$$

D
Rs. $$5200$$

Solution

Simple interest $$S.I=\dfrac{P.R.T}{100}$$

$$\Rightarrow 2100 = \dfrac{P\times 6\times 7}{100}$$

$$\Rightarrow P=\dfrac{2100\times 100}{6\times 7}$$

$$\Rightarrow P=\dfrac{2100\times 100}{42}$$

$$\Rightarrow P=50\times 100$$

$$\Rightarrow P=5000$$
Hence, the principal amount $$P=Rs.5000$$
Question 5
1 / -0

A, B and C start a business each investing Rs 20000 After 5 months A withdraw Rs 5000, B withdraw Rs 4000 and C invests Rs 6000 more At the end of the year a total profit of Rs 69900 was recorded Find the share of each

A
$$Rs.\ 20500,Rs.27200,Rs.\ 22200$$

B
$$Rs.\ 20500,Rs.25200,Rs.\ 24200$$

C
$$Rs.\ 20500,Rs.21200,Rs.\ 28200$$

D
$$Rs.\ 20500,Rs.23200,Rs.\ 26200$$

Solution

Ratio of the capitals of A, B and C = $$20000 \times 5 + 15000 \times 7 : 20000 \times 5 + 16000 \times 7 20000 \times 5 + 26000 \times 7$$
$$= 205000 : 212000 : 282000 = 205 : 212 : 282$$
$$\therefore$$ A's share $$ =Rs.(69900\times \dfrac{205}{699})=RS.20500$$
B's share $$=Rs.(69900\times \dfrac{212}{699})=RS.21200$$
C's share $$ =Rs.(69900\times \dfrac{282}{699})=RS.28200$$
Question 6
1 / -0

A shop-keeper purchases $$11$$ knives in Rs. $$10$$ and sells them at the rate of $$10$$ knives for Rs.$$11$$. He earns a profit of

A
$$11$$ $$\%$$

B
$$15$$ $$\%$$

C
$$17$$ $$\%$$

D
$$21$$ $$\%$$

Solution

C.P. of $$1$$ knife $$=\dfrac{10}{11}$$
S.P of $$1$$ knife $$= \dfrac{11}{10}$$
Profit $$=$$ S.P $$-$$ C.P
Profit =$$ \dfrac{11}{10} - \dfrac{10}{11} = \dfrac{121 - 100}{110} = \dfrac{21}{110}$$

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

Profit $$\%$$ $$ = \dfrac{\dfrac{21}{110}}{\dfrac{10}{11}} \times 100$$

$$ \Rightarrow \dfrac{21}{110} \times \dfrac{11}{10} \times 100 = 21$$ $$\%$$
Question 7
1 / -0

If the cost of $$7$$ kg of rice is Rs. $$168$$, what is the cost of $$105$$ kg of rice?

A
Rs. $$ 2,580$$

B
Rs. $$ 2,630$$

C
Rs. $$ 2,520$$

D
Rs. $$ 2,500$$

Solution

Cost of $$1$$ kg of rice $$=\dfrac{168}{7}$$
$$=Rs\ 24$$

Thus cost of $$105$$kg rice is given as $$Rs\ (24\times 105)$$ that is equal to $$Rs\ 2520$$
Question 8
1 / -0

Rajan borrowed Rs. $$5000$$ from Rakesh at simple interest. After $$3$$ years, Rakesh got Rs. $$300$$ more than what he had given to Rajan. What was the rate of interest per annum?

A
$$2\%$$

B
$$5\%$$

C
$$8\%$$

D
$$10\%$$

Solution

Given: Rajan borrowed $$Rs.5000$$ from Rakesh

Let the rate of interest be $$R\ \%$$

Then, simple interest after $$3 $$ years $$=\dfrac{5000\times 3 \times R}{100}$$

Given: Rakesh get $$Rs.300$$ more than the interest

$$\Rightarrow \dfrac{5000\times 3\times R}{100}=300$$

$$\Rightarrow R=\dfrac{300\times 100}{5000\times 3}$$

$$\Rightarrow R=2\%$$
Question 9
1 / -0

Find the rate, when $$Rs.\ 1800$$ earns an interest of $$Rs.\ 432$$ in $$3$$ years

A
$$7\%$$

B
$$6\%$$

C
$$5\%$$

D
$$8\%$$

Solution

Given:
Principal, $$P=Rs.\ 1800$$
Interest, $$I=Rs.\ 432$$
Times, $$ T=3$$ years

$$I=\dfrac{P\times R\times T}{100}$$

$$R=\dfrac {I\times 100}{P\times T}$$

$$=\dfrac {432\times 100}{1800\times 3}$$

$$=8\%$$
Question 10
1 / -0

Mr. Mittal finds that an increase in the rate of interest from $$4 \displaystyle \dfrac{7}{8}\%$$ to $$5 \displaystyle \dfrac{1}{8}\%$$ per annum increases his yearly income by Rs. $$250$$. His investment is

A
Rs. $$1,00,000$$

B
Rs. $$1,20,000$$

C
Rs. $$1,50,000$$

D
Rs. $$2,00,000$$

Solution

Let the investment be $$Rs. x$$. Then
$$x \times \displaystyle \dfrac{41}{8} \times \dfrac{1}{100} - x \dfrac{39}{8} \times \dfrac{1}{100} = 250$$

or $$2x = 200000$$

or $$x = 100000$$

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Comparing Quantities Test - 36

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Comparing Quantities Test - 36

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SHARING IS CARING

Question 1

4

8

9

None of these

Solution

Question 2

2 : 3 : 5

3 : 4 : 7

4 : 5 : 9

None of these

Solution

Question 3

Rs 330

Rs 360

Rs 380

Rs 430

Solution

Question 4

Rs. $$4400$$

Rs. $$4800$$

Rs. $$5000$$

Rs. $$5200$$

Solution

Question 5

$$Rs.\ 20500,Rs.27200,Rs.\ 22200$$

$$Rs.\ 20500,Rs.25200,Rs.\ 24200$$

$$Rs.\ 20500,Rs.21200,Rs.\ 28200$$

$$Rs.\ 20500,Rs.23200,Rs.\ 26200$$

Solution

Question 6

$$11$$ $$\%$$

$$15$$ $$\%$$

$$17$$ $$\%$$

$$21$$ $$\%$$

Solution

Question 7

Rs. $$ 2,580$$

Rs. $$ 2,630$$

Rs. $$ 2,520$$

Rs. $$ 2,500$$

Solution

Question 8

$$2\%$$

$$5\%$$

$$8\%$$

$$10\%$$

Solution

Question 9

$$7\%$$

$$6\%$$

$$5\%$$

$$8\%$$

Solution

Question 10

Rs. $$1,00,000$$

Rs. $$1,20,000$$

Rs. $$1,50,000$$

Rs. $$2,00,000$$

Solution

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