Comparing Quantities Test

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Comparing Quantities Test - 49

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Weekly Quiz Competition

Question 1
1 / -0

The question given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

By selling an article what is the profit percent gained?
I. $5\%$ discount is given on list price.
II. If the discount is not given, $20\%$ profit is gained.
III. The cost price of the articles is $\text{Rs. } 5000$ .

A
Only I and II

B
Only II and III

C
Only I and III

D
All I, II and III

E
None of these

Solution

I. Let the list price be $\text{Rs. } x$
Then, $\text{S.P.} = 95\%$ of $\text{Rs. } x = \text{Rs. } \left (x\times \dfrac {95}{100}\right ) = \text{Rs. } \dfrac {19x}{20}$
II. When $\text{S.P.} = \text{Rs. } x$ and gain $= 20\%$
Then, $\text{C.P.} =\text{Rs. } \left (\dfrac {100}{120}\times x\right ) =\text{Rs. } \dfrac {5x}{6}$
$\therefore \text{Gain} = \left (\dfrac {19x}{20} - \dfrac {5x}{6}\right ) = \left (\dfrac {57x - 50x}{60}\right ) = \dfrac {7x}{60}$
$\therefore \text{Gain}\%$ $=\left (\dfrac {7x}{60}\times \dfrac {6}{5x} \times 100\right )\%$ $= 14\%$ .
Thus, I and II only give the answer.
$\therefore$ Correct answer is (A).

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Question 2
1 / -0

A trader marks $10\%$ higher than the cost price. He gives a discount of $10\%$ on the marked price. In this kind of sales how much percent does the trader gain or lose?

A
$5\%$ gain

B
$2\%$ gain

C
$1\%$ loss

D
$3\%$ loss

Solution

Let the cost price be $\text{Rs }100$
Then the mark-up price is $10\%$ above the cost price.
Mark price $=(100+10\% \ \text{of}\ 100)=$ $\text{Rs.}$ $110$
Trader gives $10\%$ discount on the marked price, then the
Selling price $=(110-10\% \ \text{of}\ 110)=$ $\text{Rs.}$ $99$
Therefore, Loss $=$ cost price $-$ selling price
Loss $=100-99= \text{Rs }1$ on cost price of $\text{Rs }100$
Thus loss percent is $1\%$ .

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Question 3
1 / -0

Two bicycles were sold for Rs. $3990$ each, gaining $5 \%$ on one and losing $5 \%$ on the other. The gain or loss $\%$ on the whole transaction is.

A
$0.25\%$ loss

B
$2.5\%$ gain

C
$3.5\%$ gain

D
neither gain nor loss

Solution

Selling price of two bicycles $= 3990$ Rs. each

Let the cost price of a bicycle on which gain is $5\%$ $=x$
and another bicycle on which loss is $20\%$ $=y$

Solving for bicycle on which he gain
We know that, $Selling\ price = Cost\ price + profit$

$\Rightarrow 3990 = x + 5\%\ of\ x$

$\Rightarrow 3990 = x+0.05x$

$\Rightarrow 3990 = 1.05x$

$\Rightarrow x = \dfrac{3990}{1.05}$

$\therefore x = 3800\ Rs$

Now, Solving for bicycle on which he loss
We know that, $Selling\ price=Cost\ price-loss$

$\Rightarrow 3990 = y - 5\%\ of\ y$

$\Rightarrow 3990 = y - 0.05y$

$\Rightarrow 3990 = 0.95y$

$\Rightarrow y = \dfrac{3990}{0.95}$

$\therefore y = 4200\ Rs$

Now, $Total\ Cost\ price = x + y = 3800+4200 = 8000$

and $Total\ Selling\ price = 2\times3990 = 7980$

Since $Selling\ price < Cost Price$

So, In whole transaction, there is a loss and loss $= 8000-7980=20$

$\therefore Loss\ Percentage=\dfrac{Loss\times100}{Cost\ Price}=\dfrac{20\times100}{8000}=0.25\%\ loss$

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Question 4
1 / -0

Two blends of tea costing Rs $35$ per kg and Rs $40$ per kg respectively are mixed in the ratio $2 : 3$ by weight. If one-fifth of the mixture is sold at Rs $46$ per kg and the remaining at the rate of Rs $55$ per kg, find the profit percent.

A
$40$ %

B
$45$ %

C
$35$ %

D
$50$ %

Solution

Let's assume the proportional value is $x$

So, First kind of tea $= 2x$ kg and Second kind of tea $= 3x$ kg

Now, $CP=\sum(Amount\times Cost\ price\ rate)$

$\therefore\ CP=2x\times 35+3x\times 40=190x\ Rs$

Amount of mixture $=2x+3x=5x\ kg$

Given that, $\dfrac{1}{5}th\ of\ mixture=x\ kg$ sold at $46\ Rs$ per kg and remaining $(5x-x=4x\ kg)$ sold at $55\ Rs$ per kg

So, $SP=\sum(Amount\times Selling\ price\ rate)$

$\therefore\ SP=x\times 46+4x\times 55=266x\ Rs$

Now, $Profit=SP-CP=266x-190x=76x\ Rs$

$\therefore Profit\ percentage=\dfrac{Profit\times 100}{CP}=\dfrac{76x\times 100}{190x}=40\%$

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Question 5
1 / -0

A vendor bought toffees at $6$ for a rupee. How many for a rupee must he sell to gain $20$ %?

A
$3$

B
$4$

C
$5$

D
$6$

Solution

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Question 6
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
$25$ %

C
$75$ %

D
$40$ %

Solution

$CP$ of an old bicycle $=480$

Cost on repairs $=480\times {\dfrac{20}{100}}=96$

Total CP $=480+96=576$

Profit $=144$

Profit $\%=\dfrac{144}{576}\times 100=25$

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Question 7
1 / -0

A man bought two goats for Rs. $1008$ . He sold one at a loss of $20$ % and the other a profit of $44$ %. If each goat was sold for the same price, the cost price of the goat which was sold at a loss was

A
Rs. $360$

B
Rs. $648$

C
Rs. $440$

D
Rs. $568$

Solution

$\Rightarrow$ Cost price of two goats is $Rs.1008$ .
$\Rightarrow$ $80\%$ of cost price of first goat = $144\%$ of cost price of second goat.
$\Rightarrow$ cost price of first goat : cost price of second goat = $144:80=9:5$
$\Rightarrow$ Cost price of first goat= $\dfrac{9}{9+5}\times 1008=$ Rs. $648$

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Question 8
1 / -0

Raghav purchased a scooter at $\dfrac {13}{15}$ of its selling price and sold it at $12 \%$ more than its selling price. What is his gain per cent ?

A
$29 \dfrac {3}{13}$ %

B
$21 \dfrac {3}{18}$ %

C
$22 \dfrac {3}{18}$ %

D
$23 \dfrac {3}{11}$ %

Solution

Let selling price of scooter be X Rs.

Cost price for Raghav (CP) $=\dfrac{13}{15}\ of\ X=\dfrac{13X}{15}$

Selling price for Raghav is 12% more than Selling price.

$\Rightarrow SP=X+12\%\ of\ X=X+0.12X=\dfrac{28X}{25}\ Rs$

$\therefore Gain=SP-CP=\dfrac{28X}{25}-\dfrac{13X}{15}=\dfrac{168X-130X}{150}=\dfrac{38X}{150}$

$\therefore Gain\ Percentage=\dfrac{Gain\times100}{CP}=\dfrac{\dfrac{38X}{150}\times100}{\dfrac{13X}{15}}=\dfrac{380}{13}=29\dfrac{3}{13}\%$

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Question 9
1 / -0

A tradesman fixed the selling prices of goods at $30$ % above the cost price. He sells half of the stock at this price, one-quarter of his stock at a discount of $15$ % on the original selling price, and the rest at a discount of $30$ % on the original selling price. Find the gain percent altogether.

A
$5\dfrac{1}{8}$ %

B
$15\dfrac{1}{8}$ %

C
$5\dfrac{3}{8}$ %

D
$15\dfrac{3}{8}$ %

Solution

Let cost price of goods be $x\ Rs$ per unit and total unit be $y$ units.

Then total cost price (CP) $=xy\ Rs$

Selling price of goods is 30% higher than cost price.

So, Selling price of goods $=x+30\%\ of\ x=\dfrac{13x}{10}$ per units.

According to question, $\dfrac{y}{2}$ units of goods sold at selling price, $\dfrac{y}{4}$ units of goods sold at 15% discount and remaining $\dfrac{y}{4}$ units of goods sold at 30% discount.

So, Total Selling Price (SP) $=\sum(Amounts\times Selling\ price\ rate)$

$\Rightarrow SP=(\dfrac{y}{2}\times \dfrac{13x}{10})+(\dfrac{y}{4}\times (\dfrac{13x}{10}-15\%\ of\ \dfrac{13x}{10}))+(\dfrac{y}{4}\times (\dfrac{13x}{10}-30\%\ of\ \dfrac{13x}{10}))$

$\Rightarrow SP=\dfrac{13xy}{20}+(\dfrac{y}{4}\times \dfrac{221x}{200})+(\dfrac{y}{4}\times \dfrac{91x}{100})$

$\Rightarrow SP=\dfrac{520xy}{800}+\dfrac{221xy}{800}+\dfrac{182xy}{800}$

$\therefore SP=\dfrac{923xy}{800}$

Hence, $Gain=SP-CP=\dfrac{923xy}{800}-xy=\dfrac{123xy}{800}$

So, $Gain\ percentage = \dfrac{Gain\times 100}{CP}=\dfrac{\dfrac{123xy}{800}\times 100}{xy}=\dfrac{123}{8}=15\dfrac{3}{8}\%$

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Question 10
1 / -0

The shopkeeper gives a discount of $12$ % on the pair of shoes marked for Rs. $1425$ , then S.P is:

A
Rs. $1245$

B
Rs. $1445$

C
Rs. $1254$

D
Rs. $1524$

Solution

Discount $=12$ %
MP $=1425$
SP =MP -Discount
$=1425-\dfrac{12}{100} \times 1425$
$=1254$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 49

Result

Comparing Quantities Test - 49

Score

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SHARING IS CARING

Question 1

Only I and II

Only II and III

Only I and III

All I, II and III

None of these

Solution

Question 2

5%5\%5% gain

2%2\%2% gain

1%1\%1% loss

3%3\%3% loss

Solution

Question 3

0.25%0.25\%0.25% loss

2.5%2.5\%2.5% gain

3.5%3.5\%3.5% gain

neither gain nor loss

Solution

Question 4

404040%

454545%

353535%

505050%

Solution

Question 5

333

444

555

666

Solution

Question 6

505050%

252525%

757575%

404040%

Solution

Question 7

Rs. 360360360

Rs. 648648648

Rs. 440440440

Rs. 568568568

Solution

Question 8

29313 29 \dfrac {3}{13}29133​%

21318 21 \dfrac {3}{18}21183​%

22318 22 \dfrac {3}{18}22183​%

23311 23 \dfrac {3}{11}23113​%

Solution

Question 9

5185\dfrac{1}{8}581​%

151815\dfrac{1}{8}1581​%

5385\dfrac{3}{8}583​%

153815\dfrac{3}{8}1583​%

Solution

Question 10

Rs. 124512451245

Rs. 144514451445

Rs. 125412541254

Rs. 152415241524

Solution

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Question Analysis

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$5\%$ gain

$2\%$ gain

$1\%$ loss

$3\%$ loss

$0.25\%$ loss

$2.5\%$ gain

$3.5\%$ gain

$40$ %

$45$ %

$35$ %

$50$ %

$3$

$4$

$5$

$6$

$50$ %

$25$ %

$75$ %

$40$ %

Rs. $360$

Rs. $648$

Rs. $440$

Rs. $568$

$29 \dfrac {3}{13}$ %

$21 \dfrac {3}{18}$ %

$22 \dfrac {3}{18}$ %

$23 \dfrac {3}{11}$ %

$5\dfrac{1}{8}$ %

$15\dfrac{1}{8}$ %

$5\dfrac{3}{8}$ %

$15\dfrac{3}{8}$ %

Rs. $1245$

Rs. $1445$

Rs. $1254$

Rs. $1524$