Comparing Quantities Test

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Comparing Quantities Test - 50

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Weekly Quiz Competition

Question 1
1 / -0

The cost price of an article is $$\displaystyle \frac {3}{5}$$ times of its selling price. Find the loss or the gain as percent.

A
Gain : 60$$\%$$

B
Gain : 67$$\%$$

C
Gain : 33$$\%$$

D
Gain : 40$$\%$$

Solution

Let SP $$=x$$
So, CP $$=\dfrac{3}{5} x$$
$$Gain =SP -CP$$
$$=x -\dfrac{3}{5}x$$
$$=\dfrac{2}{5}x $$
$$Gain\%=\dfrac{2x}{3x}\times 100 $$
Profit $$=67$$%
Question 2
1 / -0

A book seller bought $$200$$ textbooks for Rs. $$12000$$. He wanted to sell them at a profit so that he get $$20$$ books free. At what profit per cent should he sell them?

A
$$40\%$$

B
$$20\%$$

C
$$30\%$$

D
$$10\%$$

Solution

Cost price (CP) of $$200$$ textbooks $$ =$$ Rs. $$ 12000 $$
Therefore, cost price of a book $$=\dfrac{12000}{200}=$$ Rs. $$60 $$
Profit $$=$$ Cost of $$20$$ books $$=20\times 60=$$ Rs. $$1200$$
Thus $$ \text{Profit percentage}=\dfrac{\text{profit}\times 100}{CP}=\dfrac{1200\times 100}{12000}=10\%$$
Question 3
1 / -0

A trader marks his goods at 25% above his cost price and allows a discount of $$\displaystyle12 \frac{1}{2}$$% on purchases for cash payment. The profit percent he makes is:

A
$$\displaystyle9 \frac{3}{8}$$ %

B
$$\displaystyle8 \frac{3}{8}$$ %

C
$$\displaystyle10 \frac{3}{8}$$ %

D
$$\displaystyle11 \frac{3}{8}$$ %

Solution

Let's assume cost price = X Rs

Since marked price is 25% above cost price.

$$\therefore MP=CP+25\%\ of\ CP=X+\dfrac{25X}{100}=\dfrac{5X}{4}\ Rs$$

Discount $$=12\dfrac{1}{2}\%=\dfrac{25}{2}\%$$

$$\therefore SP=MP-Discount$$

$$\Rightarrow SP=\dfrac{5X}{4}-\dfrac{25}{2}\%\ of\ \dfrac{5X}{4}$$

$$\Rightarrow SP=\dfrac{5X}{4}-\dfrac{25}{200}\times \dfrac{5X}{4}$$

$$\Rightarrow SP=\dfrac{5X}{4}-\dfrac{5X}{32}=\dfrac{35X}{32}$$

$$\therefore Profit=SP-CP=\dfrac{35X}{32}-X=\dfrac{3X}{32}\ Rs$$

$$\Rightarrow Profit\ percentage=\dfrac{profit\times 100}{CP}=\dfrac{\dfrac{3X}{32}\times 100}{X}=\dfrac{75}{8}=9\dfrac{3}{8}\%$$
Question 4
1 / -0

If a commission $$10\%$$ given on the marked price of a book, the publisher gain $$20\%$$.
If the commission is increased by $$15\%$$, the gain of publisher is

A
$$16.33\%$$

B
$$\dfrac {67}{3} \%$$

C
$$33.33\%$$

D
$$\dfrac {20}{3} \%$$

Solution

Let's assume cost price of book (CP) $$= X$$ Rs

Given that $$Gain = 20\%$$

$$\therefore SP=CP+20\%\ of\ CP=X+20\%\ of\ X=\dfrac{6X}{5}\ Rs$$

Let Marked price be $$Y$$ Rs

Given that $$Commision = 10\%$$

We know that, $$SP=MP-Commission$$

$$\Rightarrow \dfrac{6X}{5}=Y-10\%\ of\ Y=\dfrac{9Y}{10}$$

$$\Rightarrow Y=\dfrac{4X}{3}\ Rs$$

If there is no commission, then SP = MP = $$\dfrac{4X}{3}$$

$$\therefore Gain=SP-CP=\dfrac{4X}{3}-X=\dfrac{X}{3}$$

$$\Rightarrow Gain\ percentage = \dfrac{Gain\times 100}{CP}=\dfrac{\dfrac{X}{3}\times 100}{X}=\dfrac{100}{3}\%$$
Question 5
1 / -0

A manufacturer undertakes to supply $$4000$$ pieces of particular component at Rs. $$100$$ per piece. According to his estimates, even if $$10$$% fail to pass the quality tests, then he will make a profit of $$20$$%. However, as it turned out, $$50$$% of the components were rejected. What is the loss to the manufacturer ?

A
Rs. $$120,000$$

B
Rs. $$100,000$$

C
Rs. $$72,000$$

D
Rs. $$80,000$$

Solution

Total pieces $$=4000$$, Price of each$$=100$$
Given if $$10$$% fail, he will still make $$20$$% profit
$$\Rightarrow (90$$% of $$4000) \times SP=CP+\cfrac { 20 }{ 100 } CP$$
$$\Rightarrow \cfrac { 90 }{ 100 } \times 4000\times 100=CP\times \cfrac { 120 }{ 100 } $$
$$\Rightarrow CP=3,00,000$$
C.P we got is for total $$4000$$ pieces
$$\Rightarrow$$C.P of each piece$$=\cfrac { 300000 }{ 4000 } =75$$
But only $$50$$% i.e., $$2000$$ pieces were accepted
$$S.P=2000\times 100=2,00,000$$
Profit or Loss=S.P-C.P$$=200000-300000$$
$$=-100000$$ (Loss)
$$\therefore$$ The manufacturer is at a loss of Rs.$$1,00,000$$
Question 6
1 / -0

A man sells two articles for the same price for Rs. $$640$$. He earns $$20$$% profit on the first and $$10$$% profit on the second. Find the over all percent profit.

A
$$14.78$$%

B
$$14.08$$%

C
$$14.28$$%

D
$$14.58$$%

Solution

Selling price of two articles $$ = 640$$ Rs. each

Let cost price of article on which man gains $$20\%\ profit$$ be $$X$$ Rs
and another article on which man gains $$10\%\ profit$$ be $$Y$$ Rs.

Solving for first article on which man gains 20% profit
We know that, $$Selling\ price = Cost\ price + profit$$

$$\Rightarrow 640 = X + 20\%\ of\ X$$

$$\Rightarrow 640 = X+0.2X$$

$$\Rightarrow 640 = 1.2X$$

$$\Rightarrow X = \dfrac{640}{1.2}$$

$$\therefore X = \dfrac{1600}{3}\ Rs$$

Now, Solving for article on which man gains 10% profit
We know that, $$Selling\ price=Cost\ price+loss$$

$$\Rightarrow 640 = Y +10\%\ of\ Y$$

$$\Rightarrow 640 = Y + 0.1Y$$

$$\Rightarrow 640 = 1.1Y$$

$$\Rightarrow Y = \dfrac{640}{1.1}$$

$$\therefore Y = \dfrac{6400}{11}\ Rs$$

Now, $$Total\ Cost\ price = X + Y = \dfrac{1600}{3}+\dfrac{6400}{11}=\dfrac{17600+19200}{33} = \dfrac{36800}{33}\ Rs=1115.15\ Rs$$

and $$Total\ Selling\ price = 2\times640 = 1280\ Rs$$

Overall profit $$Selling\ price-Cost\ Price=1280-1115.15=164.85\ Rs$$

$$\therefore Profit\ percentage=\dfrac{profit\times100}{Cost\ price}=\dfrac{164.85\times100}{1115.15}=14.78\%$$
Question 7
1 / -0

A pirate purchased an old bicycle for $$ Rs.\ 960$$. He spent $$20 \%$$ of the cost on its repair. If he wants to earn $$ Rs\ 288$$ as net profit on it, find profit $$\%$$.

A
$$50$$%

B
$$40$$%

C
$$35$$%

D
$$25$$%

Solution

Purchase price of an old bicycle $$= Rs\ 960$$

Repair cost $$=20\%\ of\ cost=20\%\ of\ 960=\dfrac{20\times 960}{100}=192\ Rs$$

Hence, Total cost $$=960+192=1152\ Rs$$

Given that $$ Profit = 288\ Rs$$

$$\therefore Profit\ percentage = \dfrac{profit\times 100}{Total\ cost}=\dfrac{288\times 100}{1152}=25\%$$
Question 8
1 / -0

Calculate the principal when time $$= 10$$ years, interest = Rs. $$3000$$; rate $$= 5\%$$ p.a.

A
Rs. $$5000$$

B
Rs. $$6000$$

C
Rs. $$7000$$

D
Rs. $$8000$$

Solution

simple interest formula is given by:

$$S.I.=\dfrac{P\times R\times T}{100}$$

where $$S.I = $$ simple interest
$$P=$$ principle
$$R=$$ rate of interest
$$T=$$ number of years

Given, $$T=10$$ years, $$S.I=$$ Rs. $$3000$$, $$R=5\%$$

by substituting the values in the formula we get:

$$\Rightarrow$$ $$3000=\dfrac{P\times 5\times 10}{100}$$

$$\Rightarrow$$ $$P=\dfrac{3000\times 100}{5\times 10}=$$ Rs. $$6000$$

Therefore, the principle is Rs. $$6000$$.
Question 9
1 / -0

$$1\%$$ of $$1\%$$ of $$25\%$$ of $$1000$$ is :

A
$$0.25$$

B
$$0.025$$

C
$$0.00025$$

D
$$25$$

Solution

We need to find value of $$1\%\,\text{of}\,1\%\,\text{of}\,25\%\,\text{of}\,1000$$
This would be equal to $$\dfrac{1}{100}\times \dfrac{1}{100}\times \dfrac{25}{100}\times 1000$$
$$=\dfrac{25}{1000}$$
$$=0.025$$.
Question 10
1 / -0

Jenn borrowed Rs. $$5,000$$ for $$5$$ years and had to pay Rs. $$1,500$$ simple interest at the end of that time. What rate of interest did she pay?

A
$$5$$

B
$$6$$

C
$$7$$

D
$$8$$

Solution

$$\Rightarrow$$ $$P=Rs.5000,\,T=5\,years $$ and $$S.I.=Rs.1500$$
$$\Rightarrow$$ $$S.I.=\dfrac{P\times R\times T}{100}$$

$$\Rightarrow$$ $$1500=\dfrac{5000\times R\times 5}{100}$$

$$\Rightarrow$$ $$R=\dfrac{1500}{250}$$

$$\therefore$$ $$R=6\%$$

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Comparing Quantities Test - 50

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Comparing Quantities Test - 50

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SHARING IS CARING

Question 1

Gain : 60$$\%$$

Gain : 67$$\%$$

Gain : 33$$\%$$

Gain : 40$$\%$$

Solution

Question 2

$$40\%$$

$$20\%$$

$$30\%$$

$$10\%$$

Solution

Question 3

$$\displaystyle9 \frac{3}{8}$$ %

$$\displaystyle8 \frac{3}{8}$$ %

$$\displaystyle10 \frac{3}{8}$$ %

$$\displaystyle11 \frac{3}{8}$$ %

Solution

Question 4

$$16.33\%$$

$$\dfrac {67}{3} \%$$

$$33.33\%$$

$$\dfrac {20}{3} \%$$

Solution

Question 5

Rs. $$120,000$$

Rs. $$100,000$$

Rs. $$72,000$$

Rs. $$80,000$$

Solution

Question 6

$$14.78$$%

$$14.08$$%

$$14.28$$%

$$14.58$$%

Solution

Question 7

$$50$$%

$$40$$%

$$35$$%

$$25$$%

Solution

Question 8

Rs. $$5000$$

Rs. $$6000$$

Rs. $$7000$$

Rs. $$8000$$

Solution

Question 9

$$0.25$$

$$0.025$$

$$0.00025$$

$$25$$

Solution

Question 10

$$5$$

$$6$$

$$7$$

$$8$$

Solution

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