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).
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 $$1\%$$.
Question 3
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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 $$= 8000-7980=20$$

$$\therefore Loss\ Percentage=\dfrac{Loss\times100}{Cost\ Price}=\dfrac{20\times100}{8000}=0.25\%\ loss$$
Question 4
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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, $$Profit=SP-CP=266x-190x=76x\ Rs$$

$$\therefore Profit\ percentage=\dfrac{Profit\times 100}{CP}=\dfrac{76x\times 100}{190x}=40\%$$
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
Question 6
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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 $$\%=\dfrac{144}{576}\times 100=25$$
Question 7
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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. $$648$$
Question 8
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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.

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

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

$$\therefore Gain\ Percentage=\dfrac{Gain\times100}{CP}=\dfrac{\dfrac{38X}{150}\times100}{\dfrac{13X}{15}}=\dfrac{380}{13}=29\dfrac{3}{13}\%$$
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, $$Gain\ percentage = \dfrac{Gain\times 100}{CP}=\dfrac{\dfrac{123xy}{800}\times 100}{xy}=\dfrac{123}{8}=15\dfrac{3}{8}\%$$
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

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Comparing Quantities Test - 49

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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

$$5\%$$ gain

$$2\%$$ gain

$$1\%$$ loss

$$3\%$$ loss

Solution

Question 3

$$0.25\%$$ loss

$$2.5\%$$ gain

$$3.5\%$$ gain

neither gain nor loss

Solution

Question 4

$$40$$%

$$45$$%

$$35$$%

$$50$$%

Solution

Question 5

$$3$$

$$4$$

$$5$$

$$6$$

Solution

Question 6

$$50$$%

$$25$$%

$$75$$%

$$40$$%

Solution

Question 7

Rs. $$360$$

Rs. $$648$$

Rs. $$440$$

Rs. $$568$$

Solution

Question 8

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

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

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

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

Solution

Question 9

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

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

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

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

Solution

Question 10

Rs. $$1245$$

Rs. $$1445$$

Rs. $$1254$$

Rs. $$1524$$

Solution

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