Comparing Quantities Test

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Comparing Quantities Test - 30

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Question 1
1 / -0

If the selling price is doubled, the profit triples. Find the profit per cent

A
$$66\dfrac {2}{3}\%$$

B
$$100\%$$

C
$$105\dfrac {1}{3}\%$$

D
$$120\%$$

Solution

Let the $$C.P. =Rs.x$$ and $$S.P. =Rs.y$$.
Then, profit $$=Rs. (y - x)$$
If $$S.P. = 2y$$, then profit $$= 3(y - x)$$
Given, $$2y - x = 3(y - x)$$
$$\Rightarrow y = 2x \Rightarrow S.P. = 2 \times C.P. \Rightarrow$$ Profit is 100%.
Question 2
1 / -0

A man sells two horses for $$ Rs. 1485$$. The cost price of the first is equal to the selling price of the second. If the first is sold at $$20\%$$ loss and the second at $$25\%$$ gain, what is his total gain or loss (in rupees)?

A
$$Rs. 80$$ gain

B
$$Rs. 60$$ gain

C
$$Rs. 60$$ loss

D
Neither gain nor loss

Solution

Let the S.P. of the first horse $$=Rs. x$$. Then,
S.P. of the second horse $$=Rs. (1485 - x)$$
C.P. of the first horse $$=\dfrac {x\times 100}{(100-20)}=Rs \dfrac {5x}{4}$$
C.P. of the second horse $$=\dfrac {(1485-x)\times 100}{(100+25)}$$
$$=Rs \dfrac {4(1485-x)}{5}$$
Given, $$\dfrac {5x}{4}=(1485-x)$$
$$\Rightarrow 5x=4\times (1485-x)\Rightarrow 9x=4\times 1485$$
$$\Rightarrow x=4\times \dfrac {1485}{9}=Rs. 660$$
$$\therefore$$ Total C.P. $$=\dfrac {5\times 660}{4}+\dfrac {4(1485-660)}{5}$$
$$=Rs. 825+Rs. 660=Rs. 1485$$
Since S.P. $$=$$ C.P., there is no profit no loss.
Question 3
1 / -0

A tradesman sold an article at a loss of $$20\%$$. If the selling price had been increased by Rs. $$100$$, there would have been a gain of $$5\%$$. The cost price of the article was

A
Rs. $$200$$

B
Rs. $$225$$

C
Rs. $$400$$

D
Rs. $$250$$

Solution

Let the C.P. of the article be Rs. $$x$$
Then, S.P. of the article at a loss of $$20\%$$
$$=\dfrac {80}{100}\times x=$$ Rs. $$ \dfrac {80x}{100}$$
S.P. of the article at a profit of $$5\%$$
$$=\dfrac {105}{100}\times x=$$ Rs. $$ \dfrac {105x}{100}$$
According to the question, we have
$$\dfrac {80x}{100}+100=\dfrac {105x}{100}$$
$$\Rightarrow \dfrac {105x}{100}-\dfrac {80x}{100}=100$$
$$\Rightarrow x=\dfrac {100\times 100}{25}=$$ Rs. $$400$$
Question 4
1 / -0

A person sells a table at a profit of $$20\%$$. If he had bought it at $$10\%$$ less cost and sold for Rs. $$105$$ more, he would have gained $$35\%$$. The cost price of the table is

A
Rs. $$7000$$

B
Rs. $$7350$$

C
Rs. $$9200$$

D
Rs. $$8140$$

Solution

Let the C.P. of the table be Rs. x.
Then, S.P. of the table at 20% profit$$=\dfrac {120}{100}\times Rs. x=Rs \dfrac {6x}{5}$$
C.P. of the table at 10% loss $$=\dfrac {90}{100}\times Rs. x$$$$=Rs \dfrac {9x}{10}$$
S.P. of the table at 35% profit now$$=\dfrac {135}{100}\times Rs \dfrac {9x}{10}$$
Then according to the question
$$\dfrac {6x}{5}+105=\dfrac {135}{100}\times \dfrac {9x}{10}$$

$$\Rightarrow \dfrac {6x}{5}+105=\dfrac {243}{200}x$$

$$\Rightarrow \dfrac {243}{200}x-\dfrac {6}{5}x=105$$

$$\Rightarrow \left (\dfrac {243-240}{200}\right )x=105$$

$$\Rightarrow x=\dfrac {105\times 200}{3}=Rs. 7000$$.
Question 5
1 / -0

Mohan bought $$20$$ dining tables for Rs. $$12000$$ and sold them at a profit equal to the selling price of $$4$$ dining tables. The selling price of each dining table is

A
Rs. $$700$$

B
Rs. $$750$$

C
Rs. $$725$$

D
Rs. $$775$$

Solution

Profit $$=$$ (S.P. of $$20$$ tables) $$-$$ (C.P. of $$20$$ tables)
$$\Rightarrow$$ S.P. of $$4$$ tables $$=$$ S.P. of $$20$$ tables $$-$$ C.P. of $$20$$ tab1es
$$\Rightarrow$$ S.P. of $$16$$ tables $$=$$ C.P. of $$20$$ tables $$=$$ Rs. $$ 12000$$
$$\Rightarrow$$ S.P. of $$1$$ dining table $$=$$ Rs. $$ \dfrac {12000}{16}=$$ Rs. $$ 750$$
Question 6
1 / -0

A shopkeeper earns a profit of $$15$$% after selling a book at $$20$$% discount on the printed price. The ratio of the cost price and the printed price of the book is

A
$$20:23$$

B
$$23:20$$

C
$$16:23$$

D
$$23:16$$

Solution

Let the printed price of the book be Rs. $$100$$
After a discount of $$20\%$$, S.P. $$=$$ Rs. $$80 $$
Profit earned $$= 15\%$$
Thus, Cost Price of Book $$=$$ $$\displaystyle \frac{100}{115}\times 80$$ =$$ \displaystyle \frac{1600}{23}$$
Hence, (C.P) : (printed price) $$=$$ $$\displaystyle \frac{1600}{23}:100$$
$$=$$ $$16:23$$
Question 7
1 / -0

If a merchant estimates his profits as $$20$$ $$\%$$ of the selling price, what is his real profit percent.

A
$$25$$ $$\%$$

B
$$20$$ $$\%$$

C
$$22$$ $$\%$$

D
$$30$$ $$\%$$

Solution

Suppose SP $$=$$ Rs. $$100$$
Profit $$=$$ Rs. $$20$$
CP $$= 100 - 20 =$$ Rs. $$80$$
Profit $$\% = $$ $$\displaystyle\frac{\text {profit}}{\text {CP}}\,\times\, 100\,=\, \frac{20}{80}\,\times\, 100$$
$$= 25 \%$$
Question 8
1 / -0

A woman bought two parcels of toffees, the same number in each parcel. She bought the first pack at $$25$$ paise per each toffee and the second pack at $$3$$ toffees for $$65$$ paise. She mixed them together and sold at Rs. $$3.50$$ a dozen. Her gain percent is:

A
$$15\%$$

B
$$25\%$$

C
$$\displaystyle16\frac{2}{3}\%$$

D
$$12\%$$

Solution

In the first pack, the amount she pays for $$3$$ toffee $$=3\times 25=75$$ paise.
In the second pack , the amount she pays for $$3$$ toffee $$=65$$ paise
$$\therefore$$ for $$6$$ toffee she pays $$75+65=$$ Rs. $$1.40$$
And for a dozen she pay $$=1.40+1.40=$$ Rs. $$2.80$$
S.P. of $$1$$ dozen toffees $$=$$ Rs. $$3.50$$
C.P. $$<$$ S.P
Profit $$=3.50-2.80=0.70 = 70$$ paise
Profit $$\%=\dfrac{0.70}{2.80}\times 100=25\%$$
Question 9
1 / -0

Sugar is bought at Rs. $$16.20$$ per kg and sold at Rs. $$17.28$$ per kg. The gain percent is:

A
$$6 \displaystyle \frac{2}{3} \%$$

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

C
$$10 \%$$

D
$$10 \displaystyle \frac{2}{3} \%$$

Solution

C.P $$=16.20 $$ per kg, S.P$$=17.28$$ per kg
Profit $$=17.28-16.20=$$ Rs. $$1.08$$
Profit $$\%$$ $$=\dfrac{1.08}{16.20}\times 100=6\dfrac{2}{3}$$ $$\%$$
Question 10
1 / -0

By selling a transistor for Rs. $$572$$, a shopkeeper earns a profit equivalent to $$30\%$$ of the cost price of the transistor. What is the cost price of the transistor?

A
Rs. $$340$$

B
Rs. $$400$$

C
Rs. $$440$$

D
Rs. $$350$$

Solution

Let the C.P. of the transistor be Rs. $$x$$
Profit $$=30\%$$ of Rs. $$x$$ $$=$$ Rs. $$\dfrac {3x}{10}$$
S.P. $$=$$ Rs. $$ 572$$

C.P. $$+$$ Profit $$=$$ S.P.
Therefore, $$ x+\dfrac {3x}{10}=572$$

$$\Rightarrow \dfrac {13x}{10}=572$$
$$\Rightarrow x=$$ Rs. $$ \dfrac {572\times 10}{13}=$$ Rs. $$ 440$$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 30

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Comparing Quantities Test - 30

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SHARING IS CARING

Question 1

$$66\dfrac {2}{3}\%$$

$$100\%$$

$$105\dfrac {1}{3}\%$$

$$120\%$$

Solution

Question 2

$$Rs. 80$$ gain

$$Rs. 60$$ gain

$$Rs. 60$$ loss

Neither gain nor loss

Solution

Question 3

Rs. $$200$$

Rs. $$225$$

Rs. $$400$$

Rs. $$250$$

Solution

Question 4

Rs. $$7000$$

Rs. $$7350$$

Rs. $$9200$$

Rs. $$8140$$

Solution

Question 5

Rs. $$700$$

Rs. $$750$$

Rs. $$725$$

Rs. $$775$$

Solution

Question 6

$$20:23$$

$$23:20$$

$$16:23$$

$$23:16$$

Solution

Question 7

$$25$$ $$\%$$

$$20$$ $$\%$$

$$22$$ $$\%$$

$$30$$ $$\%$$

Solution

Question 8

$$15\%$$

$$25\%$$

$$\displaystyle16\frac{2}{3}\%$$

$$12\%$$

Solution

Question 9

$$6 \displaystyle \frac{2}{3} \%$$

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

$$10 \%$$

$$10 \displaystyle \frac{2}{3} \%$$

Solution

Question 10

Rs. $$340$$

Rs. $$400$$

Rs. $$440$$

Rs. $$350$$

Solution

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