Comparing Quantities Test

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Comparing Quantities Test - 56

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Weekly Quiz Competition

Question 1
1 / -0

A wholesaler bought $$120$$ watches for $$\text{Rs }30$$ each. He sold $$50\%$$ of the watches for $$\text{Rs }20$$ each, one-third at $$\text{Rs }40$$ each and the rest for $$\text{Rs }60$$. What was the wholesaler's approximate avenge profit per watch?

A
$$\text{Rs }3.3$$

B
$$\text{Rs }5$$

C
$$\text{Rs }7$$

D
$$\text{Rs }9$$

E
$$\text{Rs }11$$

Solution

C.P. of each watch $$=\text{Rs }30$$ , number of watches $$=120$$
total C.P. $$=30\times 120=\text{Rs }3600$$
Wholesaler sold $$50\%$$ ($$60$$ watches) at $$\text{Rs }20$$
S.P. of these $$60$$ watches $$(S.P_1)=60 \times 20=\text{Rs }1200=$$
$$\left(\dfrac{1}{3}\right)^{rd}$$ of $$120$$ watches are sold at $$\text{Rs }40$$
$$S.P_2=40\times 40=\text{Rs }1600$$
rest $$(120-60-40=20)$$ watches are sold at $$\text{Rs }60$$
$$S.P_3=20\times 60=\text{Rs }1200$$
Total S.P. $$=1200+1600+1200=\text{Rs }4000$$
profit $$=$$ S.P. $$-$$ C.P. $$=4000-3600=\text{Rs }400$$
Average profit per watch $$=\dfrac{400}{120}=\text{Rs }3.3$$
Question 2
1 / -0

A man buys $$100kg$$ of sugar for $$Rs. 2400$$. He sold $$1/4^{th}$$ of the stock at a loss of $$5\%$$. At what percent profit should he sell the remaining stock so as to make an overall profit of $$20\%$$ on the whole transaction?

A
$$25\%$$

B
$$27\dfrac{1}{3}\%$$

C
$$28\%$$

D
$$28\dfrac{1}{3}\%$$

Solution

Quantity of sugar $$= 100 kg$$

Cost of 100 kg sugar $$= Rs. 2400$$

Sold $${\left(\dfrac{1}{4}\right)}^{th}$$ quantity of sugar at a loss of $$5\%$$

$$\cfrac{1}{4}$$ of $$2400 = Rs. 600$$

Cost of 25 kg sugar $$= Rs. 600$$

$$Loss = C.P. - S.P.$$

$$Loss = 5 \% \; of \; 600 \; = \cfrac{(600 \times 5)}{100} = Rs. 30$$

S.P. of 25 kg sugar $$= 600 - 30 = Rs. 570$$

Profit required on whole transaction = 20 $$\%$$ + loss to be recovered of Rs. 30

$$20\ %$$ of $$2400 = Rs. 480 + Rs. 30$$

Total profit required $$= Rs. 510$$

C.P. of remaining quantity of sugar $$= 2400 - 600 = Rs. 1800$$

$$\text{Profit percent on whole transaction} = \cfrac{(510 \times 100)}{1800} = \cfrac{51000}{1800} = 28.33\% \approx 28\cfrac{1}{3} \%$$
Question 3
1 / -0

The selling price of $$18$$ pencils is the same as cost price of $$21$$ pencils. Find the gain percent.

A
$$14.2\%$$

B
$$22.6\%$$

C
$$16.1\%$$

D
$$33.3\%$$

Solution

Let $$SP$$ of each pencils be $$Rs.x$$
$$SP$$ of $$18$$ pencils be $$Rs.18x$$
Let $$CP$$ of each pencils be $$Rs.y$$
$$CP$$ of $$21$$ pencils be $$Rs.21y$$
According to the question,
$$18x=21y$$
$$\cfrac{x}{y}=\cfrac{21}{18}$$
Gain$$\%=\cfrac{SP-CP}{CP\times 100}\implies \cfrac{21-18}{18}\times100=14.2\%$$
Hence, gain$$\%=14.2\%$$.
Question 4
1 / -0

Brinda purchased $$18$$ coats at the rate of Rs. $$1500$$ each and sold them at a profit of $$6\%$$. If customer is to pay sales tax at the rate of $$4\%$$, how much will one coat cost to the customer and what will be the total profit earned by Brinda after selling all coats?

A
Rs$$1635.6$$ and Rs. $$1520$$

B
Rs$$1652.6$$ and Rs. $$1550$$

C
Rs$$1653.6$$ and Rs. $$1620$$

D
Rs$$1654.6$$ and Rs. $$1660$$

Solution

$$\Rightarrow$$$$Cost \ price \ (CP)=Rs.1500$$
Profit$$=6\%$$

$$\Rightarrow$$$$Selling \ Price \ (SP)=106\%\times Rs.1500=Rs.1590.........$$(without sales tax).

After $$4\%$$ Sales tax ,

Net $$SP=104\% \ of \ Rs.1590=Rs.1653.6$$

Net profit over $$18$$ coats$$=(1590\times 18) - (1500 \times 18)=Rs.1620$$.

(Since sales tax is paid to government and not earned as a profit by Bindra).
Question 5
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Mr. X, a business man had the income in the year $$2000$$, such that he earned a profit of $$20$$% n his investment in the business. In the year $$2001$$, his investment was less by Rs. $$5000$$ but still had the same income (Income=Investment+Profit) as that in $$2000$$. Thus, the percent profit earned in $$2001$$ increased by $$6$$%. What was his investment in $$2000$$?

A
Rs. $$1,02,000$$

B
Rs. $$1,05,000$$

C
Rs. $$1,50,500$$

D
Data inadequate

E
None of these

Solution

Let investment of Mr. X be 'I' in $$2000$$
Profit in year $$2000=20$$% on investment
$$=\cfrac { I }{ 5 } $$
$$\therefore $$ Total income in year $$2000=I+\cfrac { I }{ 5 } $$
$$=\cfrac { 6I }{ 5 } $$
Investment of Mr. X in $$2001=(I-5000)$$
Income is same in both $$2000$$ and $$2001$$
$$\therefore (I--5000)+P=\cfrac { 6I }{ 5 } $$, P is iprofit in year $$2001$$
$$P=\cfrac { I }{ 5 } +5000$$
Profit percent increased by $$6$$%, $$\therefore $$ New profit percent $$20+6=26$$%
$$\cfrac { \cfrac { I }{ 5 } +5000 }{ I-500 } =\cfrac { 26 }{ 100 } \Rightarrow 20I+5000(100)=26I-26(5000)$$
$$\Rightarrow 6I=(126)5000$$
$$\therefore I=$$Rs. $$1,05,000$$
Question 6
1 / -0

If meena gives an interest of Rs. $$45$$ for one year at $$9\%$$ rate p.a. What is the has borrowed ?

A
Rs. $$450$$

B
Rs. $$480$$

C
Rs. $$500$$

D
Rs. $$550$$

Solution

Let the amount, Meena has borrowed $$=P=$$ Principal
Interest of one year $$=Rs. 45$$
Rate, $$r=9$$% per annum
Time, $$t=1$$ year

Simple Interest $$=\cfrac{P\times r\times t}{100}$$

$$45=\cfrac{P\times 9\times 1}{100}$$

$$9P=4500$$

$$P=Rs. 500$$
Question 7
1 / -0

A shopkeeper cheats to the extent of 10% while buying as well as selling, by using false weights . His total gain is :

A
10 %

B
11 %

C
20 %

D
21%

E
$$22 \dfrac{2}{9}\%$$

Solution

So let, while buying Rs paid for n items.
But Rs made gain of 10% .Thus Rs. received
$$ 1.1 x$$ items. Now on selling again Rs.
made $$ 1.1(1.1x)= 1.21x $$
So,
the net profit Rs moles = $$ \left ( \dfrac{1.21x}{x} - 1 \right )\times 100 \% $$
$$ = 21 \%$$
Question 8
1 / -0

Amina buys a book for Rs. $$275$$ and sells it at a loss of $$15\%$$. by how much does she sell it for

A
Rs. $$230$$

B
Rs. $$233.75$$

C
Rs. $$240$$

D
Rs. $$245$$

Solution

$$\textbf{Step 1: Find the selling price of book.}$$

$$\text{The cost price of the book is Rs. }275$$
$$\text{Let the Selling price is Rs. }x$$

$$15=\cfrac{275-x}{275}\times 100$$ $$\left[\because\textbf{Loss %} \boldsymbol{=\cfrac{\text{C.P.-S.P.}}{\text{C.P.}}\times 100}\right]$$

$$275-x=\cfrac{15\times 275}{100}$$

$$275-x=41.25$$

$$x=275-41.25$$
$$x=\text{Rs }233.75$$

$$\textbf{Hence, Option B is correct.}$$
Question 9
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Hemant sold 10 sarees for a total profit of Rs.460 and 12 sarees for a total profit of Rs. 144. At what profit per saree should he sell the remaining 20 sarees so that he gets an average profit of Rs. 18 per saree ?

A
Rs. 7.40

B
Rs. 7.60

C
Rs. 7.80

D
Rs. 8
Question 10
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A man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:

A
no profit, no loss

B
$$20%$$ Profit

C
less than $$20%$$ profit

D
more than $$20%$$ profit

Solution

Let the article be worth $$ = x \ Rs.$$
Then, according to the question Cost price at 10% less value;
$$C.P. = \dfrac{(100-10)}{100}\times x = \dfrac{9x}{10} Rs.$$
Now, selling price at 10% more value;
$$S.P. = x\times \dfrac{(100+10)}{100} = \dfrac{11x}{10}Rs.$$

We know that,
$$Gain = S.P. -C.P.$$
$$ = \dfrac{11x}{10} - \dfrac{9x}{10}$$
$$ = \dfrac{2x}{10} = \dfrac{x}{5} Rs.$$

But,
$$Gain\% = \dfrac{Gain}{C.P.} \times 100$$
$$= \dfrac{(\dfrac{x}{5})}{(\dfrac{9x}{10})}\times 100$$
$$ = \dfrac{200}{9} \% = 22\dfrac{2}{9}\%$$

Therefore Option D is correct

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Comparing Quantities Test - 56

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Comparing Quantities Test - 56

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Question 1

$$\text{Rs }3.3$$

$$\text{Rs }5$$

$$\text{Rs }7$$

$$\text{Rs }9$$

$$\text{Rs }11$$

Solution

Question 2

$$25\%$$

$$27\dfrac{1}{3}\%$$

$$28\%$$

$$28\dfrac{1}{3}\%$$

Solution

Question 3

$$14.2\%$$

$$22.6\%$$

$$16.1\%$$

$$33.3\%$$

Solution

Question 4

Rs$$1635.6$$ and Rs. $$1520$$

Rs$$1652.6$$ and Rs. $$1550$$

Rs$$1653.6$$ and Rs. $$1620$$

Rs$$1654.6$$ and Rs. $$1660$$

Solution

Question 5

Rs. $$1,02,000$$

Rs. $$1,05,000$$

Rs. $$1,50,500$$

Data inadequate

None of these

Solution

Question 6

Rs. $$450$$

Rs. $$480$$

Rs. $$500$$

Rs. $$550$$

Solution

Question 7

10 %

11 %

20 %

21%

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

Solution

Question 8

Rs. $$230$$

Rs. $$233.75$$

Rs. $$240$$

Rs. $$245$$

Solution

Question 9

Rs. 7.40

Rs. 7.60

Rs. 7.80

Rs. 8

Question 10

no profit, no loss

$$20%$$ Profit

less than $$20%$$ profit

more than $$20%$$ profit

Solution

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