Comparing Quantities Test

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Comparing Quantities Test - 33

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Question 1
1 / -0

A discount of $$15\%$$ on one article is the same as a discount of $$20\%$$ on another article. The cost of the two articles can be

A
Rs $$40$$, Rs. $$20$$

B
Rs. $$60$$, Rs. $$40$$

C
Rs. $$80$$, Rs. $$60$$

D
Rs. $$50$$, Rs. $$30$$

Solution

Let the cost of the two articles be $$x$$ and $$y$$.
Then, $$15\%$$ of $$x=20\%$$ of $$y$$
$$\Rightarrow \dfrac{15}{100}\times x=\dfrac{20}{100}\times y$$
$$\Rightarrow \dfrac{x}{y}=\dfrac{20}{100}\times \dfrac{100}{15}$$
$$\Rightarrow \dfrac {x}{y}=\dfrac {20}{15}=\dfrac {4}{3}$$
$$\therefore$$ $$x$$ and $$y$$ should be in the ratio $$4: 3$$.
Then the cost price $$=$$ Rs. $$80$$ and Rs. $$60$$.
Question 2
1 / -0

If SP of an article is $$\displaystyle\frac{4}{3}$$ of its CP then the profit in the transaction is

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

B
$$\displaystyle20\frac{1}{2}\,\%$$

C
$$\displaystyle33\frac{1}{3}\,\%$$

D
$$\displaystyle25\frac{1}{2}\,\%$$

Solution

Suppose CP of article = Rs. 100
SP = $$100\,\times\, \displaystyle\frac{4}{3}\,=\, Rs. \frac{400}{3}$$
Profit = SP - CP = $$\displaystyle\frac{400}{3}\, -\, 100\, =\, Rs. \frac{100}{3}$$

Profit % = $$\displaystyle\frac{\frac{100}{3}}{100}\, \times\, 100\, =\, 33\frac{1}{3}$$ %
Question 3
1 / -0

What would be the printed price of a watch purchased at Rs. $$380$$, so that after giving $$5\%$$ discount, there is $$25\%$$ profit?

A
Rs. $$ 400$$

B
Rs. $$ 450$$

C
Rs. $$ 500$$

D
Rs. $$ 600$$

Solution

Given, C.P. $$=$$ Rs. $$ 380$$, Profit $$= 25\%$$
$$\therefore$$ S.P. $$=$$ Rs. $$ \left (\dfrac {380\times 125}{100}\right )=$$ Rs. $$ 475$$
Discount $$=$$ $$5\%$$
$$\therefore$$ M.P. $$=$$ Rs. $$ \left (\dfrac {475\times 100}{95}\right )=$$ Rs. $$ 500$$
Question 4
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 5
1 / -0

Successive discounts of $$12\dfrac {1}{2}$$% and $$7\dfrac {1}{2}$$% are given on the marked price of a cupboard. If the customer pays Rs $$2590$$, then what is the marked price?

A
Rs. $$3108$$

B
Rs. $$3148$$

C
Rs. $$3200$$

D
Rs. $$3600$$

Solution

Let the M.P. of the cupboard be Rs $$x$$.
Then, $$(100-12.5)\%$$ of $$(100-7.5)\%$$ of Rs. $$x=2590$$
$$\Rightarrow \dfrac {87.5}{100}\times \dfrac {92.5}{100}\times x=2590$$
$$\Rightarrow x=\dfrac {2590\times 100\times 100}{87.5\times 92.5}=$$ Rs. $$3200$$
Question 6
1 / -0

A shopkeeper fixes the MP of an item $$35$$% above its CP. The percentage of discount allowed to gain$$ 8$$% is:

A
$$43$$%

B
$$30$$%

C
$$20$$%

D
$$31$$%

Solution

Let $$C.P.$$ of article = Rs. $$100 $$
$$M.P.\,=\, 100\, \times\, \displaystyle\frac{135}{100}\,=\, Rs. 135$$
$$SP$$ required = $$\displaystyle100\times\frac{108}{100}\,=\, Rs. 108$$
On Rs. $$135$$ discount allowed
= Rs. $$135 -$$ Rs. $$108 =$$ Rs. $$27$$
Hence on Rs. $$100$$ discount allowed is
$$\displaystyle\frac{27}{135}\, \times\, 100\,=\, 20\%$$
Question 7
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 8
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 9
1 / -0

If the discount is $$10$$%, an item bought for Rs.$$9$$ is priced at:

A
Rs. $$11$$

B
Rs. $$10$$

C
Rs. $$8.10$$

D
Rs. $$12$$

Solution

let the M.P $$=$$ Rs. $$x$$

Then $$S.P=x-10\%$$ of $$x$$
$$\Rightarrow x-\dfrac{10x}{100}$$

$$\Rightarrow x-\dfrac{x}{10}$$

$$\Rightarrow \dfrac{9x}{10}$$
Then $$\dfrac{9x}{10}=9$$

$$\Rightarrow 9x=10\times 9$$

$$\Rightarrow x=10$$
Question 10
1 / -0

By selling an article at $$\left (\dfrac {2}{5}\right)^{th}$$ of the marked price, there is a loss of $$25\%$$. The ratio of the marked price and the cost price of the article is

A
$$2:5$$

B
$$5:2$$

C
$$8:15$$

D
$$15:8$$

Solution

Let M.P. $$=$$ Rs. $$100$$

Then S.P. $$=\dfrac{2}{5} $$ of M.P. $$=\dfrac{2}{5}\times 100=$$ Rs. $$40$$

Loss $$=25\%$$

Then, C.P. $$=\dfrac{100}{100- \text{loss} \%}\times$$ S.P.

$$\Rightarrow \dfrac{100}{100-25}\times 40$$

$$\Rightarrow \dfrac{100}{75}\times 40=$$ Rs. $$\dfrac{160}{3}$$

M.P. : C.P. $$=100:\dfrac{160}{3}=300 : 160$$

$$=15:8$$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 33

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Comparing Quantities Test - 33

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SHARING IS CARING

Question 1

Rs $$40$$, Rs. $$20$$

Rs. $$60$$, Rs. $$40$$

Rs. $$80$$, Rs. $$60$$

Rs. $$50$$, Rs. $$30$$

Solution

Question 2

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

$$\displaystyle20\frac{1}{2}\,\%$$

$$\displaystyle33\frac{1}{3}\,\%$$

$$\displaystyle25\frac{1}{2}\,\%$$

Solution

Question 3

Rs. $$ 400$$

Rs. $$ 450$$

Rs. $$ 500$$

Rs. $$ 600$$

Solution

Question 4

$$20:23$$

$$23:20$$

$$16:23$$

$$23:16$$

Solution

Question 5

Rs. $$3108$$

Rs. $$3148$$

Rs. $$3200$$

Rs. $$3600$$

Solution

Question 6

$$43$$%

$$30$$%

$$20$$%

$$31$$%

Solution

Question 7

Rs. $$150$$

Rs. $$200$$

Rs. $$250$$

Rs. $$300$$

Solution

Question 8

Rs.$$50$$

Rs.$$160$$

Rs.$$200$$

Rs. $$225$$

Solution

Question 9

Rs. $$11$$

Rs. $$10$$

Rs. $$8.10$$

Rs. $$12$$

Solution

Question 10

$$2:5$$

$$5:2$$

$$8:15$$

$$15:8$$

Solution

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