Comparing Quantities Test

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Comparing Quantities Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

An article when sold at a gain of $$5$$% yield Rs. $$15$$ more than when sold at a loss of $$5$$ $$\%$$. Its cost price would be:

A
Rs. $$150$$

B
Rs. $$200$$

C
Rs. $$250$$

D
Rs. $$300$$

Solution

Suppose the CP of the article $$=$$ Rs. $$100$$
I case :
Profit $$= 5\%$$
SP $$=$$ $$100 + 5$$ $$=$$ Rs. $$105$$
II case :
Loss $$= 5\%$$
SP $$=$$ CP $$-$$ loss $$=$$ $$100 - 5$$ $$=$$ Rs. $$95$$
Difference between two SP's
$$=$$ $$105 - 95 $$ $$=$$ Rs. $$10$$
If the difference $$=$$ Rs. $$10$$, then CP $$=$$ Rs. $$100$$
If the difference $$=$$ Rs. $$15$$, then CP $$= \frac{100}{10}\times 15=$$ Rs. $$150$$
Question 2
1 / -0

If $$5$$% more is gained by selling an article for Rs. $$350$$ than by selling it for Rs. $$340$$, the cost of the article is:

A
Rs.$$50$$

B
Rs.$$160$$

C
Rs.$$200$$

D
Rs. $$225$$

Solution

Let the C.P is =Rs. x

When S.P is Rs.340 then gain %$$=\dfrac{340-x}{x}\times 100$$

When S.P is rs.350 then gain %$$=\dfrac{350-x}{x}\times 100$$

According to the question

$$\Rightarrow \left[\dfrac{350-x}{x}\times 100 \right]-\left[\dfrac{340-x}{x}\times 100 \right]=5$$

$$\Rightarrow \dfrac{100}{x}[350-x-340+x]=5$$

$$\Rightarrow \dfrac{100}{x}[10]=5$$

$$\Rightarrow x=\dfrac{1000}{5}=200$$

Hence C.P of article is Rs.200.
Question 3
1 / -0

By selling $$20$$ mangoes a person recovers price of $$25$$ mangoes. Then profit percentage is:

A
$$20$$ $$\%$$

B
$$25$$ $$\%$$

C
$$27.5$$ $$\%$$

D
$$22.5$$ $$\%$$

Solution

Let S.P. of $$20$$ mangoes $$=$$ C.P. of $$25$$ mangoes $$=$$ Rs. $$100$$
S.P. of $$1$$ mango $$=$$ Rs. $$\displaystyle\frac{100}{20}\,=$$ Rs. $$5$$
and C.P. of $$1$$ mango $$=$$ Rs. $$\displaystyle\frac{100}{25}=$$ Rs. $$4$$
Profit $$=$$ Rs. $$(5 - 4) =$$ Rs. $$1$$
Profit $$\% =$$ $$\displaystyle\frac{1}{4}\, \times\, 100\,=\, 25\%$$
Question 4
1 / -0

A cycle is sold for Rs. 880 at a loss of 20%. For how much should it be sold to gain 10%?

A
Rs.$$1400$$

B
Rs. $$1210$$

C
Rs.$$1100$$

D
Rs. $$1000$$

Solution

SP of cycle = Rs. 880
Loss = 20%
CP of cycle = $$\displaystyle880\, \times\, \frac{100}{100\, -\, 20}\, =\, Rs. 1100$$
If gain required is 10 % then
$$SP\,=\, 1100\, \times\, \displaystyle\frac{100\, +\, 10}{100}\, =\, Rs. 1210$$
Question 5
1 / -0

400 apples were bought at Rs. 125 per hundred and were sold at a profit of Rs. 100. Find the selling price per dozen.

A
Rs. 20

B
Rs. 12

C
Rs. 18

D
None

Solution

Total CP = $$4\, \times\, 125\,=\, Rs. 500$$

$$SP = CP + profit$$

$$= 500 + 100 = Rs.\ 600$$

SP of each apples = $$\displaystyle \frac{600}{400}\,=\, \displaystyle \frac{3}{2}$$

SP of dozen apples = $$\displaystyle \frac{3}{2}\, \times\, 12$$ = Rs. 18
Question 6
1 / -0

A shopkeeper sold one fourth of his goods at a loss of $$10\%$$. He sold the remaining at a higher percent of profit to get $$\displaystyle 12\frac{1}{2}$$% profit on the whole transaction. The higher profit percent is

A
$$\displaystyle 17\frac{1}{2}$$%

B
$$\displaystyle 33\frac{1}{3}$$%

C
$$\displaystyle 22\frac{1}{2}$$%

D
$$20\%$$

Solution

Let C.P. = Rs.c $$\displaystyle$$
$$ \therefore$$ C.P. of $$\displaystyle \frac{1}{4}$$th of the goods = Rs.$$\displaystyle \frac{c}{4}$$
Loss = 10%
$$\displaystyle \therefore$$ S.P. of $$\displaystyle \frac{1}{4}$$th of the goods $$\displaystyle =\frac{\frac{c}{4}\times 90}{100}=Rs.\frac{9c}{40}$$
C.P. of $$\displaystyle \frac{3}{4}$$th of the goods = RS.$$\displaystyle \frac{3c}{4}$$
Let profit on this remaining part = P% Then
S.P. of $$\displaystyle \frac{3}{4}th$$ of the goods = $$\displaystyle \frac{\frac{3c}{4}\times (100+P)}{100}=\frac{3c}{400}(100+P)$$
Profit on the whole transaction = 12.5% $$\displaystyle$$
$$ \therefore$$ S.P. of the whole =Rs.$$\displaystyle \frac{c\times 112.5}{100}$$
$$\displaystyle \therefore$$ $$\displaystyle \frac{9c}{40}+\frac{3c}{4}+\frac{3c\times P}{400}=\frac{112.5c}{100}$$
$$\displaystyle \Rightarrow \frac{90+300+3P}{400}=\frac{112.5}{100}$$
$$\displaystyle \Rightarrow \frac{390+3P}{4}=112.5\Rightarrow 390+3P=450\Rightarrow 3P=60\Rightarrow P=20$$
Question 7
1 / -0

Mukesh purchased $$40$$ kg of wheat at Rs. $$12. 50$$ per kg and $$25$$ kg of wheat at Rs. $$15.10$$ per kg. He mixed the two qualities of wheat for selling. At what rate(in Rs.) should it be sold to gain $$10\%$$?

A
Rs. $$ 13.25$$

B
Rs. $$ 13.50$$

C
Rs. $$ 14.75$$

D
Rs. $$ 14.85$$

Solution

C.P. of the wheat $$= 40 \times$$ Rs. $$12.50 + 25 \times $$ Rs. $$15.10 = Rs.877.5$$,

Gain $$= 10\%$$

$$\displaystyle \therefore$$ S.P. of the wheat $$\displaystyle =$$ $$Rs.\dfrac{877.5\times 110}{100}$$
$$= Rs. $$965.25$$

$$\displaystyle \therefore$$ S.P. per kg of wheat $$\displaystyle =$$ Rs. $$\dfrac{965.25}{65}=$$ $$Rs.14.85$$
Question 8
1 / -0

A shopkeeper sells tea at $$10\%$$ profit and uses a weight which is $$20\%$$ less than the actual measure. His gain percent is

A
$$30\%$$

B
$$35\%$$

C
$$\displaystyle 37\frac{1}{2}$$ $$\%$$

D
$$32\%$$

Solution

Let the marked weight be $$1$$ kg.
But the real weight he uses $$= 80\%$$ of $$1$$ kg $$= 800$$ gm.
Let the C.P. of $$1$$ gm be Rs. $$1$$
Then C.P. of $$800$$ gm $$=$$ Rs. $$800$$ and C.P. of $$1000$$ gm $$=$$ Rs. $$1000$$
$$\displaystyle \therefore$$ S.P. $$\displaystyle =1000\times \frac{110}{100}=$$ Rs. $$1100$$
Gain $$=$$ Rs. $$1100 -$$ Rs. $$800 =$$ Rs. $$300$$
Gain $$\%$$ $$\displaystyle \frac{300}{800}\times 100=\frac{300}{8}\%=37\frac{1}{2}\%$$
Question 9
1 / -0

Profit earned by selling an article for Rs. $$1,060$$ is $$20$$% more than the loss incurred by selling the article for Rs. $$950$$. At what price should the article be sold to earn $$20$$% profit?

A
Rs. $$1000$$

B
Rs. $$1150$$

C
Rs. $$1,250$$

D
Rs. $$1,200$$

Solution

Let C.P. be Rs $$x$$
Then $$ (1060 - x ) = \dfrac{120}{100} \times (x-950)$$
$$\Rightarrow 10600 - 10x = 120x- 120 \times 950$$
$$\Rightarrow 220x = 220000$$
$$ \Rightarrow x = 1000$$
$$\therefore$$ Desired S.P. $$=$$ Rs. $$\left (\dfrac{120}{100} \times 1000\right) =$$ Rs. $$1200$$
Question 10
1 / -0

A shopkeeper allows a discount of 10% on the marked price. How much above the cost price must he mark his goods to gain 8%?

A
20%

B
100%

C
80%

D
None of these

Solution

let Marked price of an article be $$x$$

Discount on article $$=x-10$$%of$$ x$$

$$=x-\frac{10}{100}x$$

$$=0.9x$$

Therefore, selling price of the article$$=0.9x$$

Now, Gain % $$=\frac{sp-cp}{cp}$$

Put the value of gain % and $$sp$$ in the above equation and calculate $$cp$$.

$$\frac{8}{100}=\frac{0.9x-cp}{cp}$$

$$8cp=90x-100cp$$

$$108cp=90x$$

$$cp=\frac{90x}{108}$$

$$cp=\frac{5x}{6}$$

Therefore, cost price $$cp$$ marked above marked price($$mp$$) $$=\frac{mp-cp}{cp}\times100$$

Put the valus of $$cp$$ and $$mp$$ in the above equation
$$=\frac{x-\frac{5x}{6}}{\frac{5x}{6}}\times100$$

$$=\frac{\frac{x}{6}}{\frac{5x}{6}}$$

$$20$$%

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Comparing Quantities Test - 32

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Comparing Quantities Test - 32

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Question 1

Rs. $$150$$

Rs. $$200$$

Rs. $$250$$

Rs. $$300$$

Solution

Question 2

Rs.$$50$$

Rs.$$160$$

Rs.$$200$$

Rs. $$225$$

Solution

Question 3

$$20$$ $$\%$$

$$25$$ $$\%$$

$$27.5$$ $$\%$$

$$22.5$$ $$\%$$

Solution

Question 4

Rs.$$1400$$

Rs. $$1210$$

Rs.$$1100$$

Rs. $$1000$$

Solution

Question 5

Rs. 20

Rs. 12

Rs. 18

None

Solution

Question 6

$$\displaystyle 17\frac{1}{2}$$%

$$\displaystyle 33\frac{1}{3}$$%

$$\displaystyle 22\frac{1}{2}$$%

$$20\%$$

Solution

Question 7

Rs. $$ 13.25$$

Rs. $$ 13.50$$

Rs. $$ 14.75$$

Rs. $$ 14.85$$

Solution

Question 8

$$30\%$$

$$35\%$$

$$\displaystyle 37\frac{1}{2}$$ $$\%$$

$$32\%$$

Solution

Question 9

Rs. $$1000$$

Rs. $$1150$$

Rs. $$1,250$$

Rs. $$1,200$$

Solution

Question 10

20%

100%

80%

None of these

Solution

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