Comparing Quantities Test

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Comparing Quantities Test - 43

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Question 1
1 / -0

A shopkeeper buys an article at $$70\%$$ of its printed price. He spends $$Rs.\ 40$$ on transportation of the article. After charging Sales Tax at the rate of $$10\%$$ on the printed price, he sells the article for $$Rs.\ 7,040.$$ Find his profit as a percent to the nearest integer.

A
$$42\%$$

B
$$40\%$$

C
$$37\%$$

D
$$47\%$$

Solution

Let the printed price of the article be $$x.$$

Then according to the statement,
$$x+10\%$$ of $$x=7040$$
$$\Rightarrow \dfrac{10x+x}{10}=7040$$
$$\Rightarrow \dfrac{11x}{10}=7040$$
$$\Rightarrow x=\dfrac{70400}{11}$$
$$\Rightarrow x=Rs.\ 6400$$

$$\therefore$$ Printed price of the article is equal to $$Rs.\ 6400.$$

As given shopkeeper buys the article at $$70\%$$ of its printed price.
For shopkeeper $$CP$$ of the article $$=70\%$$ of $$6400$$
$$=\dfrac{70}{100}\times 6400$$
$$=Rs.\ 4480$$

Since he spend $$Rs.\ 40$$ on the transportation of the article,
Total cost price $$=4480+40$$
$$=Rs.\ 4520$$

$$\text{Profit}=6400-4520$$
$$=Rs.\ 1880$$

$$\text{Profit}\ \%=\dfrac{1880}{4520}\times 100$$
$$=41.59\%$$
$$\approx42\%$$
Question 2
1 / -0

Two merchants sell, each an article for Rs. $$1000$$. If merchant $$A$$ computes his profit on cost price, while merchant $$B$$ computes his profit on selling price, they end up making profits of $$25\%$$. By how much is the profit made by Merchant $$B$$ greater than that of Merchant $$A$$?

A
$$66.67$$

B
$$125$$

C
$$50$$

D
$$100$$

Solution

Merchant $$B$$ computes his profit as a percentage of selling price. He makes a profit of $$25\%$$ on selling price of Rs. $$1000$$ i.e. his profit $$=25\%$$ of $$1000=$$ Rs. $$250$$.
Merchant $$A$$ computes his profit as a percentage of cost price.
Therefore, when he makes a profit of $$25\%$$ or $$\left (\dfrac{1 }{4}\right)^{th}$$ of his cost price, then his profit expressed as a percentage of selling price $$=$$ or $$20\%$$ of selling price.
So, merchant $$A$$ makes a profit of $$20\%$$ of Rs. $$1000=$$ Rs. $$200$$.
Merchant B makes a profit of Rs. $$250$$ and merchant A makes a profit of Rs. $$200$$.
Hence, merchant $$B$$ makes Rs. $$50$$ more profit than merchant $$A$$.
Question 3
1 / -0

A man buys an article for Rs. $$27.50$$ and sells it for Rs. $$28.60$$. Find his gain percent.

A
$$4$$

B
$$5$$

C
$$2$$

D
$$10$$

Solution

Given, selling price Rs. $$28.60$$ and cost price $$=27.50$$
Gain $$=SP - CP $$
$$=$$ Rs. $$ \begin{pmatrix}28.60 - 27.50\end{pmatrix}$$
$$=$$ Rs. $$1.10$$
Gain $$\%=\begin{Bmatrix}\begin{pmatrix}\dfrac{1.10}{27.50}\end{pmatrix}\times100\end{Bmatrix}\%=4\%$$
Question 4
1 / -0

If the cost price is $$96\%$$ of the selling price, then what is profit percent?

A
$$3.13$$

B
$$5.26$$

C
$$4.17$$

D
$$5.89$$

Solution

Let selling price be $$100$$, then cost price will be $$96$$.

Thus, profit $$=S.P-C.P=4$$

Profit $$\%=\dfrac{\text {profit}}{\text{cost price}}\times 100 = \begin{pmatrix}\dfrac{4}{96}\end{pmatrix}\times100=4.17\%$$
Question 5
1 / -0

By selling a jeans for Rs. $$432$$, John loses $$4\%$$. For how much should John sell it to gain $$6\%$$?

A
Rs. $$458$$

B
Rs. $$428$$

C
Rs. $$477$$

D
Rs. $$436$$

Solution

SP of the shirt $$=432$$
Loss $$=4\%$$
Therefore, $$CP$$ of the shirt $$=\dfrac {100}{100-\text{loss} \%}\times SP$$
$$=\dfrac {100}{100-4}\times 432$$
$$=450$$
Now,$$CP=450$$, desired gain $$=6\%$$
Desired$$,SP=\dfrac {100+\text{gain} \%}{100}\times CP$$
$$=\dfrac {100+6}{100}\times 450$$
$$=477$$
Hence, the desired selling price is Rs. $$477$$.
Question 6
1 / -0

A merchant marks his goods in such a way that the profit on sale of $$50$$ articles is equal to the selling price of $$25$$ articles. What is his profit margin ?

A
$$25\%$$

B
$$50\%$$

C
$$100\%$$

D
$$66.67\%$$

Solution

Let the selling price per article be $$=$$ Rs. $$1$$
Therefore, selling price of $$50$$ articles $$=$$ Rs. $$50$$
Profit on sale of $$50$$ articles $$=$$ selling price of $$25$$ articles $$=$$ Rs. $$25$$.
S.P $$=$$Rs. $$ 50$$, Profit $$=$$ Rs. $$25$$
Therefore, CP $$=$$ Rs.$$(50-25)=$$ Rs. $$25$$
Profit $$\%=\dfrac{25}{25}\times100\%=100\%$$
Question 7
1 / -0

The cost of an article is decreased by $$15$$ $$\%$$. If the original cost is Rs. $$80$$, find the new cost.

A
$$68$$

B
$$65$$

C
$$57$$

D
$$55$$

Solution

Original cost of an article $$=$$ Rs. $$80$$
Decrease in cost is $$=15$$ $$\%$$ of Rs. $$80=\dfrac{15}{100}\times80=\dfrac{1200}{100}=$$ Rs. $$12$$
Therefore, new cost of an article $$=$$ Rs. $$80-$$ Rs. $$12=$$ Rs. $$68$$.
Question 8
1 / -0

The ratio in which tea costing Rs. $$192$$ per kg is to be mixed with tea costing Rs. $$150$$ per kg, so that the mixed tea when sold for Rs. $$194.40$$ per kg, gives a profit of $$20 \%$$

A
$$2 : 5$$

B
$$3 : 5$$

C
$$5 : 3$$

D
$$5 : 2$$

Solution

C.P of first tea $$=$$ Rs. $$192$$ per kg
C.P of second tea $$=$$ Rs. $$150$$ per kg
S.P of the mixture $$=$$ Rs. $$194.40$$ per kg.
Profit $$=20\%$$
Let C.P of the mixture be Rs. $$x$$ per kg
$$\Rightarrow x+20$$% of $$x$$ $$=194.40$$
$$\Rightarrow \dfrac{6x}{5}=194.40$$
$$\Rightarrow 6x=194.40\times 5$$
$$\Rightarrow x=\cfrac{972}{6}$$
$$\Rightarrow x=$$ Rs. $$162$$ per kg
Let $$N$$ kg is the first tea and $$N$$ kg is the second tea
Then using Alligation, we have
First Tea $$=162-150=12$$
Second tea $$=192-162=30$$
$$\Rightarrow \dfrac{M}{N}=\dfrac{12}{30}$$
$$\Rightarrow N:M=2:5$$
Question 9
1 / -0

The price of a TV is Rs. $$13,000$$. The sales tax on it is $$12\%$$. Find the amount that Vinod will have to pay if he buys it.

A
Rs. $$14560$$

B
Rs. $$2620$$

C
Rs. $$1456$$

D
Rs. $$1560$$

Solution

Sales tax $$=$$ Price $$\times$$ Tax Rate
$$=\dfrac{12}{100} \times 13000=1560$$
Final price $$=13000+1560=14560$$
Therefore, the amount that Vinod will have to pay will be Rs. $$14560$$.
Question 10
1 / -0

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

A
$$ $ 1$$

B
$$ $ 2$$

C
$$ $ 3$$

D
$$ $ 4$$

E
$$ $ 12$$

Solution

$$\Rightarrow$$ Let number of towels bought for $$\$120$$ be $$n$$.

$$\Rightarrow$$ So price of single towel $$=\$\dfrac{120}{n}$$

$$\Rightarrow$$ Now price of $$1$$ towel increases by $$\$1$$

$$\Rightarrow$$ So, new price of single towel $$=\$\dfrac{120}{n}+1$$

$$\Rightarrow$$ Number of towel that could be bought at this price = $$n-10$$

$$\Rightarrow$$ So, new price of single towel = $$\dfrac{120}{(n-10)}$$

So, by equating both new price of single towel,

$$\Rightarrow$$ $$\dfrac{120}{n}+1=\dfrac{120}{(n-10)}$$

$$\Rightarrow$$ $$\dfrac{(120+n)}{n}=\dfrac{120}{(n-10)}$$

$$\Rightarrow$$ $$n^2-10n-1200=0$$

$$\Rightarrow$$ $$(n-40)(n+30)=0$$

$$\Rightarrow$$ $$n=40$$ or $$n=-30$$

$$\Rightarrow$$ Number of towels is $$40$$.

$$\Rightarrow$$ Current price per towel = $$\dfrac{120}{40}=\$\,3$$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 43

Result

Comparing Quantities Test - 43

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SHARING IS CARING

Question 1

$$42\%$$

$$40\%$$

$$37\%$$

$$47\%$$

Solution

Question 2

$$66.67$$

$$125$$

$$50$$

$$100$$

Solution

Question 3

$$4$$

$$5$$

$$2$$

$$10$$

Solution

Question 4

$$3.13$$

$$5.26$$

$$4.17$$

$$5.89$$

Solution

Question 5

Rs. $$458$$

Rs. $$428$$

Rs. $$477$$

Rs. $$436$$

Solution

Question 6

$$25\%$$

$$50\%$$

$$100\%$$

$$66.67\%$$

Solution

Question 7

$$68$$

$$65$$

$$57$$

$$55$$

Solution

Question 8

$$2 : 5$$

$$3 : 5$$

$$5 : 3$$

$$5 : 2$$

Solution

Question 9

Rs. $$14560$$

Rs. $$2620$$

Rs. $$1456$$

Rs. $$1560$$

Solution

Question 10

$$ $ 1$$

$$ $ 2$$

$$ $ 3$$

$$ $ 4$$

$$ $ 12$$

Solution

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