Comparing Quantities Test

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Comparing Quantities Test - 28

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Question 1
1 / -0

A trader gains $$15\%$$ after selling an item at $$10\%$$ discount on the printed price. The ratio of the cost price and the printed price is

A
$$18 : 23$$

B
$$17 : 18$$

C
$$17 : 23$$

D
$$18 : 25$$

Solution

Let the printed price of item be Rs. $$100$$.
After discount of $$10\%$$ SP $$=$$ Rs. $$90$$ profit earned $$= 15\%$$
C.P of item $$= \dfrac{100}{115}\times 90 = \dfrac{1800}{23}$$
Hence, CP : Printed Price $$ = \dfrac{1800}{23}:100 = 18:23$$
Question 2
1 / -0

A car worth Rs. $$\ 1,50,000$$ was sold by $$X$$ to $$Y$$ at $$5 \%$$ profit. $$Y$$ sold the car back to $$X$$ at $$20 \%$$ loss. Therefore who gained in the entire transaction?

A
$$X$$ gained Rs. $$ 31500$$

B
$$X$$ lost Rs. $$ 43500$$

C
$$X$$ gained Rs. $$ 3150$$

D
$$X$$ lost Rs. $$ 315000$$

Solution

The cost price of car for $$X=$$ Rs. $$150000$$
Then selling price to $$X$$ at $$5\%$$ profit $$=$$ cost price of car to $$y$$ $$=$$ $$\dfrac{150000\times 105}{100}=$$ Rs. $$ 157500$$
But $$Y$$ sell car to $$X$$ at $$20\%$$ loss
Then selling price of car to $$Y$$ $$=$$ cost price of car $$x$$ back $$=$$ $$\dfrac{157500\times 80}{100}= $$ Rs. $$126000$$
Then Profit to $$X$$ in the entire transaction $$=157500-126000=$$ Rs. $$31500$$.
Question 3
1 / -0

John bought a car for a certain sum of money. He spent $$10 \%$$ of the cost on repairs and sold the car for a profit of Rs. $$ 11000$$. How much did he spend on repairs, if he made a profit of $$20 \%$$?

A
Rs. $$4000$$

B
Rs. $$4400$$

C
Rs. $$5000$$

D
Rs. $$5500$$

Solution

Let C.P $$=$$ Rs. $$x$$.
Then, cost on repairs $$= 10\%$$ of $$x =$$ $$\dfrac {x}{10}$$
$$\therefore $$ Total cost $$=$$ $$x+\dfrac {x}{10}=\dfrac {11x}{10}$$
Now $$20\%$$ of $$\dfrac {11x}{10}=11000$$
$$\Rightarrow \dfrac {20}{100}\times \dfrac {11x}{10}=11000\Rightarrow x=50,000$$
$$\therefore $$ Expenditure on repairs $$=10\%$$ of C.P.
$$= 10$$ $$\%$$ of Rs. $$50,000$$ $$=\dfrac{10}{100}\times 50,000=$$ Rs. $$5000.$$
Question 4
1 / -0

A man bought a second hand car for Rs. $$76000$$ and a TV, for Rs. $$27500$$. He sold the car at a gain of $$15\%$$ and the T.V. at a loss of $$12\%$$. Find the total amount gained or lost from the two transactions.

A
lost Rs. $$1800$$

B
gained Rs. $$1800$$

C
gained Rs. $$8100$$

D
lost Rs. $$8100$$

Solution

Total $$C.P.$$ of Car and TV $$ 76000 + 27500 = 103500$$
Car he sold on $$15\%$$ profit , so $$S.P.$$ of Car $$= 76000 + 76000 \times \dfrac{15}{100} = 76000+11400 = 87400$$
TV he sold on $$12\%$$ loss, $$S.P.$$ of TV $$= 27500 - 27500 \times \dfrac{12}{100} = 27500 - 3300 = 24200$$
Total Salling price $$= 87400 + 24200 = 111600$$
$$Gain = SP - CP$$
$$ = 111600 - 103500 = 8100$$
Question 5
1 / -0

A man wanted to sell on article with $$20 \%$$ profit; but he actually sold at $$20 \%$$ loss for Rs. $$480$$. At what price did he want to sell it to earn the profit.

A
Rs. $$ 720$$

B
Rs. $$ 840$$

C
Rs. $$600$$

D
Rs. $$ 750$$

Solution

Let the C.P. of the article be Rs. $$x$$.
Then, S.P. $$=$$ Rs. $$\dfrac {x\times (100-20)}{100}$$

$$\Rightarrow 480=\dfrac {x\times 80}{100}$$

$$\Rightarrow x=\dfrac{480\times 100}{80}$$
$$\Rightarrow x=$$ Rs. $$600$$
$$\therefore $$ S.P. at $$20 \%$$ profit $$=$$ Rs. $$\dfrac {600\times (100+20)}{100}$$
$$=\dfrac {600\times 120}{ 100 }=$$ Rs. $$720$$
Question 6
1 / -0

A man sold an article at a loss of $$20 \%$$. If he had sold it for Rs. $$12$$ more, then he would have gained $$ 10\%$$. The cost price of the article is

A
Rs. $$60$$

B
Rs. $$40$$

C
Rs. $$ 30$$

D
Rs. $$22$$

Solution

Assume the cost of article is $$x$$
the person sold at $$20\%$$ loss
$$Loss$$ $$\%$$ $$ = \dfrac{C.P-S.P}{C.P}= \dfrac{x-S.P}{x}= \dfrac{20}{100}$$
$$\therefore$$ $$S.P$$ $$= 0.8$$ $$x$$
If he had sold it for Rs. $$12$$ more, then he would have gained $$10\%$$.
$$Gain$$ $$\%$$ $$ = \dfrac{S.P-C.P}{C.P}= \dfrac{(0.8x+12)-x}{x}= \dfrac{10}{100}$$
$$\therefore 12-0.2x=0.1x$$
$$\therefore 12=0.3x$$
$$\therefore x=40$$
Question 7
1 / -0

Richa purchased an article at $$\displaystyle \frac{4}{5}$$ of its list price and sold it for $$20 \%$$ more than the list price. Richa's profit per cent was

A
$$50 \%$$

B
$$40 \%$$

C
$$30 \%$$

D
$$25 \%$$

Solution

Let list price of article be Rs. $$100$$
$$\therefore$$ Cost Price $$= \dfrac{4}{5} \times 100 =$$ Rs. $$80$$

$$\therefore$$ Selling Price $$= \dfrac{120}{100} \times 100 =$$ Rs. $$120$$

$$\Rightarrow$$ Profit $$= 120-80 =$$ Rs. $$40$$

$$\therefore$$ Profit $$\%$$ $$= \dfrac{Profit}{C.P.} \times 100$$
$$= \dfrac{40}{80}\times 100 = 50\%$$
Question 8
1 / -0

An item costing Rs. $$ 840$$ was sold by a shopkeeper at a gain of $$10 \%$$ and it was again sold by the new buyer at a loss of $$5 \%$$.The final selling price of the item is:

A
Rs. $$ 877.80$$

B
Rs. $$798$$

C
Rs. $$ 924$$

D
Rs. $$ 37.80$$

Solution

$$C.P.$$ $$=$$ Rs. $$840$$
$$Gain$$ $$=10\%$$

$$S.P.$$ $$=\dfrac{100+\text {gain percentage}}{100}\times$$ $$C.P$$

$$S.P.$$ $$=\dfrac{100+10}{100}\times 840$$

$$\Rightarrow \dfrac{110}{100}\times 840=$$ Rs. $$924$$

Selling price of the shopkeeper is the cost price of the new buyer.

Then $$C.P.$$ $$=$$ Rs. $$924$$

$$Loss$$ $$=5\%$$

$$S.P.$$ $$=\dfrac{100-\text {loss percentage}}{100}\times$$ $$C.P.$$

$$S.P$$ $$=\dfrac{100-5}{100}\times 924$$

$$\Rightarrow \dfrac{95}{100}\times 924=$$ Rs. $$877.80$$

Hence, final $$S.P. $$=Rs. $$877.80$$
Question 9
1 / -0

A trader purchased an old bicycle for Rs. $$ 480$$. He spent $$20 \%$$ of the cost on its repair. If he wants to earn Rs. $$144$$ as net profit on it, find profit $$\%$$.

A
$$50\%$$

B
$$48\%$$

C
$$96\%$$

D
$$100\%$$

Solution

Cost price $$=$$ Rs. $$480$$
Repair cost $$= 20\%$$ of Rs. $$480$$ $$=\dfrac{20}{100}\times 480=$$ Rs. $$96 $$
$$\therefore $$Total cost $$=$$ C.P. $$+$$ Repair cost
$$\Rightarrow$$ Rs. $$480 +$$ Rs. $$ 96 =$$ Rs. $$576$$
Net profit $$=$$ Rs. $$144$$
$$\therefore $$ S.P. = Total cost + Net profit
$$\Rightarrow $$ Rs. $$576 +$$ Rs. $$ 144 =$$ Rs. $$ 720$$
Profit $$=$$ S.P. $$-$$ C.P.
$$=720-480=$$ Rs. $$240$$
Now profit $$\% =$$ $$=\dfrac {240}{480}\times $$ $$100 =50\%$$
Question 10
1 / -0

The profit earned after selling an article for Rs. $$625$$ is the same as loss incurred after selling the article for Rs. $$435$$. What is the cost price of the article?

A
Rs $$530$$

B
Rs $$520$$

C
Rs $$540$$

D
Rs $$550$$

Solution

Let the $$C.P.$$=Rs $$x$$
Then according to the question
$$625-x=x-435$$
$$2x=625+435$$
$$2x=1060$$
$$x=530$$
Hence $$C.P.$$ of the article =Rs.$$530$$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 28

Result

Comparing Quantities Test - 28

Score

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Rank

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SHARING IS CARING

Question 1

$$18 : 23$$

$$17 : 18$$

$$17 : 23$$

$$18 : 25$$

Solution

Question 2

$$X$$ gained Rs. $$ 31500$$

$$X$$ lost Rs. $$ 43500$$

$$X$$ gained Rs. $$ 3150$$

$$X$$ lost Rs. $$ 315000$$

Solution

Question 3

Rs. $$4000$$

Rs. $$4400$$

Rs. $$5000$$

Rs. $$5500$$

Solution

Question 4

lost Rs. $$1800$$

gained Rs. $$1800$$

gained Rs. $$8100$$

lost Rs. $$8100$$

Solution

Question 5

Rs. $$ 720$$

Rs. $$ 840$$

Rs. $$600$$

Rs. $$ 750$$

Solution

Question 6

Rs. $$60$$

Rs. $$40$$

Rs. $$ 30$$

Rs. $$22$$

Solution

Question 7

$$50 \%$$

$$40 \%$$

$$30 \%$$

$$25 \%$$

Solution

Question 8

Rs. $$ 877.80$$

Rs. $$798$$

Rs. $$ 924$$

Rs. $$ 37.80$$

Solution

Question 9

$$50\%$$

$$48\%$$

$$96\%$$

$$100\%$$

Solution

Question 10

Rs $$530$$

Rs $$520$$

Rs $$540$$

Rs $$550$$

Solution

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