Comparing Quantities Test

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Comparing Quantities Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

Satyanarayana buys a watch for Rs. 1125 and sells it for Rs. 1250. The profit percentage was

A
$$11\dfrac {1}{9}\%$$

B
$$10\%$$

C
$$20\%$$

D
$$9\%$$

Solution

Given: Cost price of a watch $$=Rs.1125$$

Selling price $$=Rs. 1250$$

Since Selling price > Cost price

$$\therefore$$ Profit = Selling price $$-$$ Cost price

$$\Rightarrow$$ Profit $$= 1250 - 1125 = Rs.125$$

Now, Profit percentage $$= \dfrac{\mathrm{profit}}{\mathrm{Cost\ Price}}\times 100 $$

$$= \dfrac{125\times 100}{1125} $$

$$= 11\dfrac{1}{9}\%$$
Question 2
1 / -0

If 3 articles are sold for the cost price of4, then what is the profit percentage?

A
$$33\frac {1}{3}$$%

B
$$30\frac {1}{3}$$%

C
$$63\frac {1}{3}$$%

D
$$3\frac {1}{3}$$%

Solution

Let the C.P. of 1 article $$= Rs. 1$$.
Then, S.P. of 3 articles = C.P. of 4 articles $$=Rs. 4$$
C.P. of 3 articles $$=Rs. 3$$
Profit $$= Rs. 4 - Rs. 3 =Rs. 1$$
Profit % $$=\frac {1}{3}\times 100=33\frac {1}{3}$$%
Question 3
1 / -0

The marked price of a pen is Rs. $$60$$.After allowing a discount of $$10 \%$$, the merchant makes a profit of $$20 \%$$. What is the cost price of the pen?

A
Rs. $$ 40$$

B
Rs. $$ \ 45$$

C
Rs. $$60$$

D
Rs. $$80$$

Solution

Let the cost price of a pen Rs. $$100$$
The marchant make profit $$20\%$$, then selling price $$=$$ Rs. $$100+20=120$$
Marked price Rs. $$60$$. Allowing discount $$10\%$$ then selling price $$=$$ $$\dfrac{60\times 90}{100}=54$$ Rs
So, cost price $$=$$ $$\dfrac{54\times 100}{120}=$$ Rs. $$45$$
Question 4
1 / -0

A machine is sold at a profit of $$10\%$$. Had it been sold for Rs. $$40$$ less, there would have been a loss of $$10\%$$ . What was the cost price?

A
Rs. $$175$$

B
Rs. $$200$$

C
Rs. $$225$$

D
Rs. $$250$$

Solution

Let the cost price, C.P. be Rs. $$x$$
Profit $$= 10\%$$
Hence, S.P. $$= 1.1(x) =$$ Rs. $$ 1.1x$$
If a loss has been incurred, then the selling price of the machine would be Rs. $$0.9x$$.
Difference in selling prices $$= 40$$
$$1.1x - 0.9x = 40$$
$$0.2x = 40$$ or $$x = 200$$
The cost price of the machine is Rs. $$ 200$$.
Question 5
1 / -0

A owned an, article worth Rs. $$10, 000$$. He sold it to $$B$$ at a profit of $$10\%$$ based on the worth of the article. $$B$$ sold the article back to $$A$$ at a loss of $$10\%$$. How much did $$A$$ make in these transactions?

A
Rs. $$1800$$

B
Rs. $$1560$$

C
Rs. $$1320$$

D
Rs. $$1100$$

Solution

C.P of the article for $$A$$ $$=$$ Rs. $$10,000$$
Profit $$=10\%$$
Selling price of the article by $$A$$ to $$B$$ $$=$$ Rs. $$\dfrac {110}{100}\times 10000=$$ Rs. $$11000$$
C.P of the article for $$B$$ $$=$$ Rs. $$11000$$
Loss $$=10\%$$
Selling price of the article by $$B$$ to $$A$$ $$=$$ Rs. $$\dfrac {90}{100}\times 11000=$$ Rs. $$ 9900$$
$$\therefore$$ Profit earned by $$A$$ $$=$$ Rs. $$ (11000-9000)=$$ Rs. $$1100$$.
Question 6
1 / -0

If Ashok makes a profit of $$25$$% on the selling price, what will be his profit on C.P.?

A
$$40$$%

B
$$20$$%

C
$$33\dfrac {1}{3}$$%

D
$$25$$%

Solution

Let Selling price be Rs. $$x$$
$$\therefore$$ Profit $$=25$$ $$\%$$ of $$x=\dfrac {x}{4}$$
$$\Rightarrow$$ C.P. $$=x-\dfrac {x}{4}=\dfrac {3x}{4}$$
Profit per cent on C.P. $$=\left (\dfrac {x}{4}\div \dfrac {3x}{4}\right )\times 100$$
$$=\dfrac {x}{4}\times \dfrac {4}{3x}\times 100$$
$$=33\dfrac {1}{3}$$ $$\%$$
Question 7
1 / -0

A merchant has $$1000$$ kg of sugar, part of which he sells at $$8\%$$ profit and the rest at $$18\%$$ profit. He gains $$14\%$$ on the whole. The quantity of sugar sold at $$18\%$$ profit is

A
$$560$$ kg

B
$$600$$ kg

C
$$400$$ kg

D
$$640$$ kg

Solution

Let the C.P. of sugar be Rs. $$x$$ per kg.
Then, C.P. $$=$$ Rs. 1$$000 x$$
Let the sugar sold at $$8\%$$ gain by $$y$$ kg.
Then, sugar sold at $$18\%$$ gain $$= (1000 - y)$$ kg
$$\therefore \left (\dfrac {108}{100}\times xy\right )+\left [\dfrac {118}{100}\times x(1000-y)\right ]=\dfrac {114}{100}\times 1000x$$
$$\Rightarrow \dfrac {108y}{100}+1180-\dfrac {118y}{100}=1140$$
$$\Rightarrow \dfrac {10y}{100}=40$$
$$\Rightarrow y=400$$
$$\therefore$$ Quantity sold at 18% gain $$=(1000-400)$$ kg
$$=600$$ kg.
Question 8
1 / -0

Ram mixes $$15$$ kg of sugar purchased with the rate, off Rs. $$8.00$$ per kg with $$25$$ kg of sugar purchased at the rate of Rs. $$10.00$$ per kg. At what rate per kg should Ram sell the mixture to get a profit of $$3$$ per kg?

A
Rs. $$12.25$$

B
Rs. $$15.75$$

C
Rs. $$18.18$$

D
Rs. $$19.75$$

Solution

C.P. of $$40$$ kg of sugar $$=$$ Rs. $$ (15 \times 8 + 25\times 10) =$$ Rs. $$ 120 + $$ Rs. $$ 250 =$$ Rs. $$ 370$$
$$\therefore$$ C.P. of $$1$$ kg of sugar $$=$$ Rs. $$ \dfrac {370}{40}=$$ Rs. $$ 9.25$$
$$\therefore$$ S.P. of $$1$$ kg of sugar $$=$$ Rs. $$ 9.25+$$ Rs. $$ 3=$$ Rs. $$ 12.25$$
Question 9
1 / -0

A shopkeeper sells an article at a loss of $$12\dfrac {1}{2}\%$$, Had he sold it for Rs. $$51.80$$ more than he would have earned a profit of $$6\%$$. The cost price of the article is

A
Rs. $$280$$

B
Rs. $$300$$

C
Rs. $$380$$

D
Rs. $$400$$

Solution

Let the C.P. of the article be Rs. $$x$$
According to the question, we have
S.P. at $$6\%$$ profit $$-$$ S.P. at $$12\dfrac {1}{2}\%$$ loss $$=$$ Rs. $$51.80$$
$$\Rightarrow \dfrac {x\times (100+6)}{100}-\dfrac {x\times (100-12.5)}{100}=51.80$$
$$\Rightarrow \dfrac {106x}{100}-\dfrac {87.5x}{100}=51.80$$
$$\Rightarrow \dfrac {18.5x}{100}=51.80 \Rightarrow x=\dfrac {51.80\times 100}{18.5}=280$$
Question 10
1 / -0

Mohan lent some amount of money at $$9\%$$ simple interest and an equal amount of money at $$10\%$$ simple interest each for $$2$$ years. If his total interest was Rs. $$760$$, what amount was lent in each case?

A
Rs. $$1700$$

B
Rs. $$1800$$

C
Rs. $$1900$$

D
Rs. $$2000$$

Solution

Let the amount lent in each case be Rs. $$x$$
$$\Rightarrow \dfrac{x\times9\times2}{100}+\dfrac{x\times10\times2}{100}=760$$
$$\Rightarrow \dfrac{18x}{100}+\dfrac{20x}{100}=760$$
$$\Rightarrow\;38x=76000$$
$$\Rightarrow\;x=2000$$

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Comparing Quantities Test - 28

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Comparing Quantities Test - 28

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SHARING IS CARING

Question 1

$$11\dfrac {1}{9}\%$$

$$10\%$$

$$20\%$$

$$9\%$$

Solution

Question 2

$$33\frac {1}{3}$$%

$$30\frac {1}{3}$$%

$$63\frac {1}{3}$$%

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

Solution

Question 3

Rs. $$ 40$$

Rs. $$ \ 45$$

Rs. $$60$$

Rs. $$80$$

Solution

Question 4

Rs. $$175$$

Rs. $$200$$

Rs. $$225$$

Rs. $$250$$

Solution

Question 5

Rs. $$1800$$

Rs. $$1560$$

Rs. $$1320$$

Rs. $$1100$$

Solution

Question 6

$$40$$%

$$20$$%

$$33\dfrac {1}{3}$$%

$$25$$%

Solution

Question 7

$$560$$ kg

$$600$$ kg

$$400$$ kg

$$640$$ kg

Solution

Question 8

Rs. $$12.25$$

Rs. $$15.75$$

Rs. $$18.18$$

Rs. $$19.75$$

Solution

Question 9

Rs. $$280$$

Rs. $$300$$

Rs. $$380$$

Rs. $$400$$

Solution

Question 10

Rs. $$1700$$

Rs. $$1800$$

Rs. $$1900$$

Rs. $$2000$$

Solution

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