Comparing Quantities Test

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Comparing Quantities Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

The gain or loss percent when a carriage, which cost Rs. $$4000$$, is sold for Rs. $$5000$$ is:

A
$$10$$ $$\%$$ loss

B
$$25$$ $$\%$$ loss

C
$$25$$ $$\%$$ profit

D
$$35$$ $$\%$$ profit

Solution

C.P $$=$$ Rs. $$4000$$,S.P $$=5000$$
S.P $$>$$ C.P
$$\therefore \text {Profit}=5000-4000=$$ Rs. $$1000$$
Profit $$\% =$$ $$\displaystyle \frac{\text {profit}}{\text {CP}} \times 100$$
$$= \displaystyle \frac{1000}{4000} \times 100 = 25 \%$$
Question 2
1 / -0

A man bought two old scooters for Rs. $$18000$$. By selling one at a profit of $$25\%$$ and the other at a loss of $$20\%$$, he neither gains nor loses. Find the cost price of each scooter.

A
$$12000, 6000$$

B
$$8000, 10000$$

C
$$11000, 7000$$

D
$$13000, 5000$$

Solution

Let the C.P. of the $$1^{st}$$ scooter $$=$$ Rs. $$ x$$.
Then, C.P. of the $$2^{nd}$$ scooter $$=$$ Rs. $$ (18000 - x)$$
S.P. of $$1^{st}$$ scooter $$=$$ Rs. $$ x\times \dfrac {125}{100}=$$ Rs. $$ \dfrac {5x}{4}$$
S.P. of $$2^{nd}$$ scooter $$=$$ Rs. $$ (18000-x)\times \dfrac {80}{100}$$ $$=$$ Rs. $$ \dfrac {4}{5}(18000-x)$$
Since Mohan neither gains nor loses, his total S.P. $$=$$ Total C.P.
$$\Rightarrow \dfrac {5x}{4}+\dfrac {4}{5}(18000-x)=18000$$
$$\Rightarrow \dfrac {5x}{4}-\dfrac {4x}{5}=18000-14400=3600$$
$$\Rightarrow \dfrac {25x-16x}{20}=3600\Rightarrow 9x=3600\times 20$$
$$\Rightarrow x=\dfrac {3600\times 20}{9}=8000$$
$$\therefore$$ C.P. of $$1^{st}$$ scooter $$=$$ Rs. $$ 8000$$
C.P. of $$2^{nd}$$ scooter $$=$$ Rs. $$ 10,000$$.
Question 3
1 / -0

Half of $$1$$ percent written as a decimal is

A
$$0.2$$

B
$$0.02$$

C
$$0.05$$

D
$$0.005$$

Solution

Half of $$ 1\%$$ in decimals
It will be $$\displaystyle \frac {1}{2} \times 1 \% = \displaystyle \frac {1}{2}\times \frac {1}{100}$$
$$ = \displaystyle \frac {1}{200}= 0.005$$
Question 4
1 / -0

A publisher sells books to a retail dealer at Rs. $$5$$ a copy but allows $$25$$ copies to be counted as $$24$$. If the retailer sells each of the $$25$$ copies at Rs. $$6$$, his profit percent is:

A
$$20 \%$$

B
$$25 \%$$

C
$$24 \%$$

D
$$40 \%$$

Solution

Gain $$\% =$$ $$\displaystyle\frac{\text{S.P.}\,-\, \text{C.P.}}{\text{C.P.}}\,\times\, 100$$
The cost of $$25$$ copies to the retailer $$=$$ $$5\, \times\, 24$$ $$=$$ Rs. $$120$$.
The S.P. of $$25$$ copies $$=$$ $$6\, \times\, 25$$ $$=$$ Rs. $$150$$
Profit $$\%=\displaystyle\frac{150\,-\, 120}{120}\,\times\, 100\,=\, 25%$$

$$=\dfrac{30}{120} \times100$$

$$=\dfrac{1}{4}\times100$$
$$=25\%$$
Question 5
1 / -0

If SP of an article is $$\displaystyle\frac{4}{3}$$ of its CP then the profit in the transaction is

A
$$\displaystyle\frac{1}{3}\,\%$$

B
$$\displaystyle20\frac{1}{2}\,\%$$

C
$$\displaystyle33\frac{1}{3}\,\%$$

D
$$\displaystyle25\frac{1}{2}\,\%$$

Solution

Suppose CP of article = Rs. 100
SP = $$100\,\times\, \displaystyle\frac{4}{3}\,=\, Rs. \frac{400}{3}$$
Profit = SP - CP = $$\displaystyle\frac{400}{3}\, -\, 100\, =\, Rs. \frac{100}{3}$$

Profit % = $$\displaystyle\frac{\frac{100}{3}}{100}\, \times\, 100\, =\, 33\frac{1}{3}$$ %
Question 6
1 / -0

A man bought goods worth Rs. 6,000 and sold half of them at a gain of 10%. At what gain percent must he sell the remainder to get a gain of 25% on the whole?

A
$$40\%$$

B
$$25\%$$

C
$$35\%$$

D
$$20\%$$

Solution

Total CP = Rs. 6,000
Profit = 25%
Overall SP = $$6000\, \times \, \displaystyle\frac{100\, +\, 25}{100}\,=\, Rs. 7,500$$
SP of half of the goods= $$3000\,\times\, \displaystyle\frac{100\, +\, 10}{100}\,=\, Rs. 3300$$
SP of remaining half goods$$=7500-3300=4200$$
Profit on remaining half goods costing Rs. 3000$$=4200-3000=1200$$
Profit % = $$\displaystyle\frac{1200}{3000}\,\times\, 100\,=\, 40$$%
Question 7
1 / -0

Jatin bought a refrigerator with $$20\%$$ discount on the labelled price. If he woud have bought it with $$25\%$$ discount, he could have saved Rs. $$500$$. At what price did he buy the refrigerator?

A
Rs. $$5,000$$

B
Rs. $$10,000$$

C
Rs. $$12,500$$

D
Rs. $$15,000$$

Solution

$$\Rightarrow$$ Let actual price of refrigerator is $$Rs.x$$
$$\Rightarrow$$ The cost of refrigerator to jatin after 20% discount $$=\dfrac{80}{100}\times x=\dfrac{4x}{5}$$
$$\Rightarrow$$ Cost of refrigerator to jatin after 25% discount $$=\dfrac{75}{100}\times x=\dfrac{3x}{4}$$
$$\Rightarrow$$ Then according to the question,
$$\Rightarrow$$ $$\dfrac{4x}{5}-\dfrac{3x}{4}=500$$

$$\Rightarrow$$ $$\dfrac{16x-15x}{20}=500$$

$$\therefore$$ $$x=20\times 500=10000$$
Question 8
1 / -0

If a company sells a car with a marked price of Rs. $$2,72,000$$ and gives a discount of $$4\%$$ on Rs. $$2,00,000$$ and $$2.5\%$$ on the remaining amount of Rs. $$72,000$$, then the actual price charged by the company for the car is

A
Rs. $$2,50,000$$

B
Rs. $$2,55,000$$

C
Rs. $$2,60,100$$

D
Rs. $$2,62,200$$

Solution

M.P. $$=$$ Rs. $$2,72,000$$.
Discount $$=$$ Rs. $$[(4\%$$ of $$2,00,000)+ (2.5\%$$ of $$72,000)]$$

$$=\left [\left (\dfrac{4}{100}\times 200000)+(\dfrac{2.5}{100}\times 72000\right)\right]$$
$$= $$ Rs. $$(8,000 + 1,800)$$
$$=$$ Rs. $$9,800. $$
Therefor, actual price $$=$$ Rs. $$(2,72,000 - 9,800)$$
$$=$$ Rs. $$2,62,200.$$
Question 9
1 / -0

The selling price of $$4$$ articles is same as the C.P of $$5$$ articles. Then profit percent is ____

A
$$25\%$$

B
$$20\%$$

C
$$18\%$$

D
None of these

Solution

Let C.P. of $$1$$ article is Rs. $$x$$.
$$\Rightarrow$$ C.P of $$5$$ articles $$=$$ Rs. $$5x$$
Given, C.P of $$5$$ articles $$=$$ S.P. of $$4$$ articles
$$\Rightarrow$$ S.P of $$4$$ articles $$=$$ Rs. $$5x$$
$$\Rightarrow$$ S. P of $$1$$ articles $$=$$ Rs. $$\displaystyle\frac{5}{4}x$$
Profit $$=$$ $$\displaystyle\frac{5}{4}x\,-\, x=$$ Rs. $$\dfrac{x}{4}$$
Profit $$\% =$$ $$\left ( \displaystyle \frac{\displaystyle \frac{x}{4}}{x}\, \times\, 100 \right )\%\,=\, 25\%$$
Question 10
1 / -0

A shopkeeper marks his goods at $$40$$% above the cost price and allows a discount of $$40$$% on the marked price. His loss or gain is:

A
no loss and no gain

B
$$16$$% loss

C
$$16$$% gain

D
$$20$$% gain

Solution

Let the CP of articles be Rs. 100
Loss % = $$\displaystyle\frac{40\, \times\, 40}{100}\, =\, 16%$$

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Comparing Quantities Test - 31

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Comparing Quantities Test - 31

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SHARING IS CARING

Question 1

$$10$$ $$\%$$ loss

$$25$$ $$\%$$ loss

$$25$$ $$\%$$ profit

$$35$$ $$\%$$ profit

Solution

Question 2

$$12000, 6000$$

$$8000, 10000$$

$$11000, 7000$$

$$13000, 5000$$

Solution

Question 3

$$0.2$$

$$0.02$$

$$0.05$$

$$0.005$$

Solution

Question 4

$$20 \%$$

$$25 \%$$

$$24 \%$$

$$40 \%$$

Solution

Question 5

$$\displaystyle\frac{1}{3}\,\%$$

$$\displaystyle20\frac{1}{2}\,\%$$

$$\displaystyle33\frac{1}{3}\,\%$$

$$\displaystyle25\frac{1}{2}\,\%$$

Solution

Question 6

$$40\%$$

$$25\%$$

$$35\%$$

$$20\%$$

Solution

Question 7

Rs. $$5,000$$

Rs. $$10,000$$

Rs. $$12,500$$

Rs. $$15,000$$

Solution

Question 8

Rs. $$2,50,000$$

Rs. $$2,55,000$$

Rs. $$2,60,100$$

Rs. $$2,62,200$$

Solution

Question 9

$$25\%$$

$$20\%$$

$$18\%$$

None of these

Solution

Question 10

no loss and no gain

$$16$$% loss

$$16$$% gain

$$20$$% gain

Solution

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