Comparing Quantities Test

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Comparing Quantities Test - 54

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Weekly Quiz Competition

Question 1
1 / -0

Choose the correct answer from the alternative given.
If the annual rate of simple interest increases from 10% to 12.5% . A mans yearly income increases by Rs. 1250. his principal (in rupees) is:

A
50,000

B
45,000

C
60,000

D
65,000

Solution

Change in Rate of interest= $$\left ( \dfrac{25}{2} - 10 \right )\%= \dfrac{5}{2}\%$$
According to the question, $$\dfrac{5}{2}$$% of principal = Rs. 1250
Hence, Principal = $$\dfrac{1250 \times 2 \times 100}{5}$$ = Rs. 50000
Question 2
1 / -0

A shopkeeper mixes two varieties of Tea, one costing Rs. $$40$$/kg and another Rs. $$50$$/kg in the ratio $$3:2$$. if he sells the mixed variety of Tea at Rs. $$48$$/kg, his gain or loss percent is

A
$$48.4$$% gain

B
$$48.4$$% loss

C
$$10$$% gain

D
$$10$$% loss

Solution

Average CP of Mixed Tea when Mixed in Ratio $$3:2$$
$$=\cfrac { 40\times 3+50\times 2 }{ 3+2 } =\cfrac { 220 }{ 5 } =Rs.44$$
Wen SP=Rs. $$48/kg$$
$$=\cfrac { 4 }{ 44 } \times 100=9.09\approx 10$$% gain
Question 3
1 / -0

If some articles are bought at prices ranging from Rs. 200 to Rs. 350 and are sold at prices ranging from Rs. 300 to Rs. 425, what is the maximum possible profit that might be made in selling 16 such articles?

A
Rs. 3600

B
Rs. 1200

C
Rs. 800

D
Rs. 400

Solution

Maximum profit will be if we purchase in minimum
price & sell in maximum price.
Minimum price for purchasing = Rs 200
Maximum price for purchasing = Rs 425
Net profit on 1 article $$ 425 - 200 = Rs\, 225 $$
Net profit on 16 article $$ = 225 \times 16 = Rs \,3600 $$
Question 4
1 / -0

A farmer took a loan at 12% p.a. at S.I. After 4 years he settled the loan by paying Rs. 2,442. What was the principal amount?

A
Rs. 1,542

B
Rs. 1,600

C
Rs. 1,650

D
Rs. 1,550

Solution
Question 5
1 / -0

A trader sells rice at a profit of $$20$$% and uses weights which are $$10$$% less than the correct weight. The total gain earned by him is:

A
$$22\cfrac{2}{9}$$%

B
$$35$$%

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

D
$$30$$%

Solution

Let us consider a packet of rice maked $$1\text{ kg}.$$ But its actual weight is $$90\%$$ of $$1000\text{ gm}=900\text{ gm}.$$

Let C.P of each gram of rice is $$\text{Rs. }1.$$ Then, C.P of this packet will be $$\text{Rs. }900.$$

S.P of this packet will be $$120\%$$ of C.P of $$1\text{ kg}.$$ So,
$$S.P=\cfrac { 120 }{ 100 } \times 1000$$
$$=\text{Rs. }1200$$

$$\therefore$$ Gain %$$\left( \cfrac { 300 }{ 900 } \times 100 \right) =33\cfrac { 1 }{ 3 } $$%
Question 6
1 / -0

A shopkeeper sells a T.V. set of $$\text{Rs }16560$$ at $$10\%$$ discount on its marked price and earns $$15\%$$ profit. If no discount is offered, then what will be his present profit?

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

B
$$\dfrac{250}{9}\%$$

C
$$\dfrac{27}{9}\%$$

D
$$\dfrac{500}{9}\%$$

Solution

Cost price of the article$$=\text{Rs }16560$$
let marked price be $$\text{Rs }x$$
discount $$=10\% $$
$$\text{S.P.=M.P.}\left(\dfrac{100-\text{discount %}}{100}\right)$$
$$=x\left(\dfrac{100-10}{100}\right)$$
$$=\dfrac{9x}{10}$$
Profit $$=15\%$$
Profit $$\%=\dfrac{\text{Profit}}{C.P.}\times 100$$ Where, Profit $$=$$ Selling price $$- $$ Cost price

$$\implies 15=\dfrac{S.P.-C.P.}{C.P.}\times 100$$
$$\implies 15\times 16560=\left(\dfrac{9x}{10}-16560\right)\times 100$$
$$\implies 15\times 1656=9x-165600$$
$$\implies 9x=165600+24840=190440$$
$$\implies x=21160$$
$$\therefore ~M.P. =21160$$
If no discount is offered then $$S.P.=M.P.$$
$$\therefore Profit =S.P.-C.P.$$
$$=21160-16560$$
$$=4600$$
$$\therefore Profit ~\% =\dfrac{Profit}{C.P.}\times 100$$
$$=\dfrac{4600}{16560}\times 100\%$$

$$=\dfrac{250}{9}\%$$
$$\therefore$$ Profit is $$\dfrac{250}{9}\%$$
Question 7
1 / -0

The sale price of an article including taxes is $$Rs.\ 616.$$ The rate of sales tax is $$10\%.$$ If the shopkeeper has made a profit of $$12\%.$$ find the cost price

A
$$Rs.\ 500$$

B
$$Rs.\ 450$$

C
$$Rs.\ 600$$

D
$$Rs.\ 550$$

Solution

Let us assume that the sales price and cost price of the article is $$x$$ and $$y.$$

$$\begin{aligned}{}SP + Tax& = 616\\x + \frac{{10x}}{{100}}& = 616\\\frac{{11x}}{{10}} &= 616\\x& = \frac{{616 \times 10}}{{11}}\\ &=Rs.\ 560\end{aligned}$$

And,
$$\begin{aligned}{}CP + Profit &= SP\\y + \frac{{12y}}{{100}}& = 560\\\frac{{28y}}{{25}} &= 560\\y& = \frac{{560 \times 25}}{{28}}\\ &=Rs.\ 500\end{aligned}$$

Hence, the cost price of the article is $$Rs.\ 500.$$
Question 8
1 / -0

A shirt was sold at a profit of 15$$\%$$. If its cost had been 5$$\%$$ less and it had been sold for Rs. 21 less, then the profit would have been 10$$\%$$. Find the cost of the shirt.

A
$$Rs.\ 210$$

B
$$Rs.\ 220$$

C
$$Rs.\ 100$$

D
$$Rs.\ 200$$

Solution

Given that:
A shirt was sold at a profit of $$15\%$$.
If the cost had been $$5\%$$ less, and it had been sold for $$Rs.\ 21$$ less, then the profit would have been $$10\%$$.

To find out:
The cost of the shirt.

Let the cost of the shirt be $$Rs.\ x$$.
We know that, $$S.P.=\dfrac{(profit\%+100)C.P.}{100}$$
Here, $$profit\%=15$$

$$\therefore\ S.P.=\dfrac{(15+100)x}{100}\\$$
$$\Rightarrow S.P.=1.15x\\$$

Now, if the cost is $$5\%$$ less, then,
$$C.P.=95\%\ of\ x\\$$
$$\Rightarrow C.P.=\dfrac{95}{100}x\\$$
$$\therefore \ C.P.=0.95x\\$$
Also, the selling price is $$Rs. \ 21$$ less.
$$\therefore\ S.P.=1.15x-21\\$$
In this case, the profit would have been $$10\%$$, as given in the problem.

Now, we know that, $$profit\%=\dfrac{S.P.-\ C.P.}{C.P.}\times 100$$

$$\therefore \ 10=\dfrac{(1.15x-21)-0.95x}{0.95x}\times 100\\$$
$$\Rightarrow 10=\dfrac{1.15x-21-0.95x}{0.95x}\times 100\\$$
$$\Rightarrow 10\times 0.95x=(0.20x-21)\times 100\\$$
$$\Rightarrow 9.5x=20x-2100\\$$
$$\Rightarrow 20x-9.5x=2100\\$$
$$\Rightarrow 10.5x=2100\\$$
$$\Rightarrow x=\dfrac{2100}{10.5}\\$$
$$\therefore \ x=Rs.\ 200\\$$

Hence, the cost of the shirt is $$Rs.\ 200$$.
Question 9
1 / -0

$$P$$ sells a table to $$Q$$ at a profit of $$10$$% and $$Q$$ sells it to $$R$$ at a profit of $$12$$%. If $$R$$ pays Rs. $$246.40$$ for it, then how much had $$P$$ paid for it?

A
$$200.00$$

B
$$300.00$$

C
$$248.00$$

D
$$346.00$$

Solution

Let $$P$$ paid for table $$=$$ Rs. $$P$$
After all $$R$$ paid =Rs. $$246.40$$
According to the question,
$$246.40=P\left[ \cfrac { 110 }{ 100 } \right] \left[ \cfrac { 112 }{ 100 } \right] $$
$$P=\cfrac { 246.40\times 100\times 100 }{ 110\times 112 }$$
$$=\cfrac { 246400 }{ 11\times 112 }$$
$$ =Rs.200$$
Question 10
1 / -0

A shopkeeper offers successive discounts of $$20$$%, $$10$$% and $$5$$% respectively on a Titan watch which is marked at Rs.$$1500$$. He offers successive discounts of $$20$$%. $$20$$% and $$10$$% espectively on a Ajanta watch which is marked at Rs. $$2000$$. What is the difference between their selling price?

A
Rs. $$152$$

B
Rs. $$126$$

C
Rs. $$26$$

D
Rs $$0$$

Solution

Selling price of Titan watch
= $$0.8 \times 0.9 \times 0.95 \times 1500 = Rs. 1026$$
Selling price of Ajanta watch
= $$0.8 \times 0.8 \times 8.9 \times 2000 = Rs. 1152$$
Difference is selling price = Rs.$$ (1152 - 1026) = Rs. 126$$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 54

Result

Comparing Quantities Test - 54

Score

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Rank

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SHARING IS CARING

Question 1

50,000

45,000

60,000

65,000

Solution

Question 2

$$48.4$$% gain

$$48.4$$% loss

$$10$$% gain

$$10$$% loss

Solution

Question 3

Rs. 3600

Rs. 1200

Rs. 800

Rs. 400

Solution

Question 4

Rs. 1,542

Rs. 1,600

Rs. 1,650

Rs. 1,550

Solution

Question 5

$$22\cfrac{2}{9}$$%

$$35$$%

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

$$30$$%

Solution

Question 6

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

$$\dfrac{250}{9}\%$$

$$\dfrac{27}{9}\%$$

$$\dfrac{500}{9}\%$$

Solution

Question 7

$$Rs.\ 500$$

$$Rs.\ 450$$

$$Rs.\ 600$$

$$Rs.\ 550$$

Solution

Question 8

$$Rs.\ 210$$

$$Rs.\ 220$$

$$Rs.\ 100$$

$$Rs.\ 200$$

Solution

Question 9

$$200.00$$

$$300.00$$

$$248.00$$

$$346.00$$

Solution

Question 10

Rs. $$152$$

Rs. $$126$$

Rs. $$26$$

Rs $$0$$

Solution

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