Comparing Quantities Test

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Comparing Quantities Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of $$20\%$$ on the marked price, he still has a gain of $$10\%$$?

A
$$10\%$$

B
$$25.5\%$$

C
$$30\%$$

D
$$37.5\%$$

Solution

Let the cost price of the good be $$\text{Rs. }100.$$
Selling price when profit is $$10\%=\left(100+\cfrac { 10 }{ 100 } \times 100\right)= \text{Rs. }110$$

Let the marked price is $$\text{Rs. }x.$$
After giving a discount of $$20 \%$$ , the new selling price $$= x-\left ( \dfrac{20x}{100} \right ) $$
The shopkeeper gains $$10 \%$$ after giving the discount. Thus,
$$\left [ x\,-\left ( \dfrac{20x}{100} \right ) \right ]\,=\,110$$
$$\Rightarrow \dfrac{4x}{5}=110$$
$$\Rightarrow x=\dfrac{110\times5}{4}$$
$$\Rightarrow x=\text{Rs. }137.5$$

So. this implies that the marked price of the good is equal to $$\text{Rs. }137.5.$$
Hence, the required increase $$\text{Rs. }137.5 - \text{Rs. }100 =\text{Rs. }37.5$$.
Or we can say that the required marked price should be $$\text{Rs. }37.5\%$$ more than that of the cost price.
Question 2
1 / -0

A greedy businessman cheats both the seller and buyer by $$20\%$$. His real profit is:

A
$$43\%$$

B
$$45\%$$

C
$$44\%$$

D
$$40\%$$

Solution

Let actual printed $$C.P. = Rs.125$$
Price paid by the business man = $$80\% ~of~ 125$$
Profit for him at the time of buying $$20\% ~of~ 125 = Rs. 25$$
S.P. of the businessman = $$120\% ~of~ Rs.125$$
Profit for him at the time of selling $$20\% ~of~ 125 = Rs.25$$
Total profit $$=Rs.50$$
$$\therefore $$ profit % $$= \dfrac{50}{125} \times 100 = 40\%$$
Question 3
1 / -0

Twenty identical articles are bought at 8 for Rs. 48 and all of them are sold at 5 for Rs. 37.50. Find the profit percent made.

A
12%

B
17%

C
25%

D
29%

Solution

Cost price of $$ 8 $$ articles $$ = Rs 48 $$
=> Cost price of $$ 1 $$ article $$ = Rs \dfrac {48}{8} = 6 $$
And Cost price of $$ 8 $$ articles $$ = Rs 6 \times 20 = Rs 120 $$

Selling price of $$ 5 $$ articles $$ = Rs 37.50 $$
=> Selling price of $$ 1 $$ article $$ = Rs \dfrac {37.5}{5} = Rs 7.5 $$
And Selling price of $$ 20 $$ articles $$ = Rs 7.5 \times 20 = Rs 150 $$

Now, Profit % $$ = \dfrac {S.P. - C.P.}{C.P.} \times 100 = \dfrac {150 - 120}{120} \times 100 = \dfrac {30}{120} \times 100 = 25 $$ %
Question 4
1 / -0

Find the profit per cent or loss per cent made in each of the following cases, when :
by selling 20 identical articles, a shopkeeper gains equal to C.P. of 5 articles.

A
Loss $$= 12$$%

B
Loss $$= 30$$%

C
Profit $$= 22$$%

D
Profit $$= 25$$%

Solution

Let Cost price of $$ 1 $$ article $$ = Rs x $$
=> And Cost price of $$ 20 $$ articles $$ = Rs 20x $$
Given, Gain on selling $$ 20 $$ articles $$ = $$ Cost price of $$ 5 $$ articles $$ = Rs 5x $$
Now, Profit % $$ = \dfrac {Profit}{C.P.} \times 100 = \dfrac {5x}{20x} \times 100 = \dfrac {1}{4} \times 100 = 25 $$ %
Question 5
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 6
1 / -0

Nikita bought $$30$$ kg of wheat at the rate of Rs. $$ 4.75$$ per kg, $$40$$ kg of wheat at the rate of Rs. $$4.25$$ per kg and mixed them. She sold the mixture at the rate of Rs. $$4.45$$ per kg. What was her total profit or loss in the transaction?

A
Rs. $$1$$ loss

B
Rs. $$1$$ profit

C
Rs. $$3.50$$ loss

D
Rs. $$3.50$$ profit

Solution

C.P.of wheat $$=$$ $$30 \times 4.75 + 40 \times 4.25$$
$$\Rightarrow 142.50+ 170 =$$ Rs. $$312.50$$
S.P. of wheat $$=$$ $$70 \times 4.45 =$$ Rs. $$311.50$$
$$\because $$C.P. $$>$$ S.P.
$$\therefore$$ Loss $$= 312.50 - 311.50=$$ Rs. $$1$$
Question 7
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 8
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 9
1 / -0

A shopkeeper purchased 300 pens and sold one out of four pens at no loss or profit. He sold the remaining pens at a profit of 20 %. What is his overall profit or loss percent on the whole transaction ?

A
15 % profit

B
15 % loss

C
12 % profit

D
12 % loss

Solution

Total number of pens $$= 300$$
Pens sold at no loss no profit $$= \dfrac{300}{4}$$
$$= 75$$
Pens sold at $$20 %$$ profit $$=$$ $$300 - 75
$$= 225$$
Let C.P. of one pen $$= Rs\ 1$$
C.P. of 225 pens $$= Rs\ 225$$
Total Profit $$= 20 % of 225 = \dfrac{20}{100} \times 225 = 45$$
Total S.P. $$=$$ CP + Profit
Total S.P. $$= 225 + 45 = 270$$

Now, Including the pens sold at no profit and no loss,
Total CP $$= 225 + 75 = 300$$
Total SP $$= 270 + 75 = 345$$
Profit % $$= \dfrac{45}{300} \times 100 = 15 \%$$
Hence, option 'A' is correct.
Question 10
1 / -0

By selling a transistor for $$Rs. \ 572$$, a shopkeeper earns a profit equivalent to $$30 \%$$ of the cost price of the transistor. What is the cost price of the transistor?

A
$$Rs. 340$$

B
$$Rs. 300$$

C
$$Rs. 400$$

D
$$Rs. 440$$

Solution

Let the C.P be Rs. $$100$$
Profit $$=30\%$$ of $$100$$ $$=\dfrac{30}{100}\times 100=$$ Rs. $$30$$
Then S.P $$=100+30=$$ Rs. $$130$$
if S.P is $$130$$, then C.P $$=$$ Rs. $$100$$
If S.P is $$572$$, then C.P$$=\dfrac{100}{130}\times 572=$$ Rs. $$440$$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 25

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Comparing Quantities Test - 25

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SHARING IS CARING

Question 1

$$10\%$$

$$25.5\%$$

$$30\%$$

$$37.5\%$$

Solution

Question 2

$$43\%$$

$$45\%$$

$$44\%$$

$$40\%$$

Solution

Question 3

12%

17%

25%

29%

Solution

Question 4

Loss $$= 12$$%

Loss $$= 30$$%

Profit $$= 22$$%

Profit $$= 25$$%

Solution

Question 5

Rs. $$4000$$

Rs. $$4400$$

Rs. $$5000$$

Rs. $$5500$$

Solution

Question 6

Rs. $$1$$ loss

Rs. $$1$$ profit

Rs. $$3.50$$ loss

Rs. $$3.50$$ profit

Solution

Question 7

Rs. $$ 720$$

Rs. $$ 840$$

Rs. $$600$$

Rs. $$ 750$$

Solution

Question 8

Rs. $$60$$

Rs. $$40$$

Rs. $$ 30$$

Rs. $$22$$

Solution

Question 9

15 % profit

15 % loss

12 % profit

12 % loss

Solution

Question 10

$$Rs. 340$$

$$Rs. 300$$

$$Rs. 400$$

$$Rs. 440$$

Solution

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