Comparing Quantities Test

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Comparing Quantities Test - 23

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Question 1
1 / -0

Rajan borrowed Rs. 50,000 from Rakesh at simple interest. After 3 years, Rakesh got Rs. 3000 more than what he had given to Rajan. What was the rate of interest per annum?

A
2%

B
5%

C
8%

D
10%

Solution

$$\Rightarrow$$ Here, we have $$P=Rs.50,000,\, T=3\, years$$ and $$S.I.=Rs.3000$$
$$\Rightarrow$$ $$Simple\, Interest=\dfrac{P\times R\times T}{100}$$

$$\Rightarrow$$ $$3000=\dfrac{50000\times R\times 3}{100}$$

$$\Rightarrow$$ $$R=\dfrac{3000\times 100}{50000\times 3}$$

$$\therefore$$ $$R=2\%$$
Question 2
1 / -0

The manufacturer A of a certain item sells it to a wholesaler at a profit of 20% on his manufacturing cost. The wholesaler sells it to a retailer at a profit of 25% and the retailer sells it to a consumer at a profit of 20%. The price paid by the consumer over and above manufacturing cost will be

A
65%

B
80%

C
85%

D
90%

Solution

Let the manufacturing cost be Rs. $$x$$.
Then the wholesaler's cost price $$= x+\cfrac{20}{100}x = Rs. \cfrac{6x}{5}$$
Retailer's cost price $$= \cfrac{6x}{5}+\cfrac{25}{100}.\cfrac{6x}{5} = Rs. \cfrac{3x}{2}$$
Finally, consumer's purchasing price
$$= \cfrac{3x}{2}+\cfrac{20}{100}\times \cfrac{3x}{2} = Rs. \cfrac{9x}{5}$$
Thus, on the manufacturing cost of Rs. $$x$$, the consumer pays $$(\cfrac{9x}{5}-x) = Rs. \cfrac{4x}{5}$$ over and above.
$$\therefore$$ % price paid by consumer over and above manufacturing cost $$= \cfrac{4x}{5}\times\cfrac{1}{x} \times 100 = 80$$.
Question 3
1 / -0

A and B invest Rs. 200 and Rs. 300, respectively, in a business for a period of three years and two years, respectively. Then the profit will be divided into the ratio of

A
$$4 : 3$$

B
$$2 : 3$$

C
$$1 : 1$$

D
$$6 : 5$$

Solution

Interest earned $$\propto$$ Amount invested $$\times$$ Time

$$\therefore$$ Profit of A $$:$$ Profit of B $$= 200\times 3 : 300 \times 2$$
$$= 1:1$$
Question 4
1 / -0

A shopkeeper purchases 11 pens for Rs. 10 and sells them at the rate of Rs. 11, then the profit is

A
8%

B
9%

C
10%

D
11%
Question 5
1 / -0

If a radio is sold at Rs. $$972$$, then profit is $$8\%$$. If it is sold at Rs. $$872$$, then there is a loss of

A
Rs. $$28$$

B
Rs. $$25$$

C
Rs. $$20$$

D
Rs. $$15$$

Solution

Let the cost price of the radio is $$Rs. x$$.
Condition I:-
Selling price of radio $$= Rs. 972$$
Profit $$\% = 8 \%$$
Therefore,
$$972 - x = \cfrac{8}{100} x$$
$$\Rightarrow \cfrac{2}{25}x + x = 972$$
$$\Rightarrow \cfrac{2x + 25x}{25} = 972$$
$$\Rightarrow x = \cfrac{972}{27} \times {25}$$
$$\Rightarrow x = 900$$
Hence the cost price of radio is $$Rs. 900$$
Condition II:-
Selling price of radio $$= Rs. 872$$
Cost price of radio $$= Rs. 900 \quad \left( \text{Given} \right)$$
Therefore,
Loss $$=$$ Cost price $$-$$ Selling price
$$\therefore$$ Loss $$= 900 - 872 = Rs. 28$$
Hence when the radio is sold at $$Rs. 872$$, then there is a loss of $$Rs. 28$$.
Question 6
1 / -0

A shopkeeper mixes 80 kg sugar worth of Rs. 6.75 per kg with 120 kg of sugar worth of Rs. 8 per kg. He earns a profit of 20% by selling the mixture. He sells it at the rate.

A
Rs. 7.50 per kg

B
Rs. 9 per kg

C
Rs. 8.20 per kg

D
Rs. 8.85 per kg

Solution

Total cost $$=80\times 6.75+120\times 8=Rs. 1500$$
Selling price $$=1500\times \dfrac {120}{100}=Rs. 1800$$
S.P. per kg $$=\dfrac {1800}{200}=Rs.9$$
Question 7
1 / -0

If the selling price of $$16$$ items is the same as the cost price of $$20$$ items, then there is a

A
Loss of $$20\%$$

B
Loss of $$25\%$$

C
Gain of $$20\%$$`

D
Gain of $$25\%$$

Solution

Let SP of $$1$$ item is equal to $$Rs.\;1.$$ Then, SP of $$16$$ items is equal to $$Rs.\;16.$$

We are given that cost price of $$20$$ items is equal to $$Rs.\;16.$$
Then, C.P. of $$1$$ item will be,
$$\dfrac{16}{20}=Rs.\;0.8$$

So, profit on each item is,
$$SP-CP=1-0.8$$
$$=Rs.\;0.2$$

$$\begin{aligned}{}\text{Gain percentage} &= \frac{{Gain}}{{CP}} \times 100\\ &= \frac{{0.2}}{{0.8}} \times 100\\ &= 25\% \end{aligned}$$
Question 8
1 / -0

A started business with Rs. 4,500 and B joined afterward with Rs. 3,000. If the profits at the end of one year were divided in the ratio 2 : 1, respectively, then B would have joined A for business after

A
1 month

B
2 months

C
3 months

D
4 months

Solution

A's 1 month's investment $$= Rs. (4500\times 12)$$
$$= Rs. 54,000$$
Let B joins after $$x$$ months.
$$\therefore$$ B's 1 month's investment $$= Rs.3,000 (12 -x)$$
By hypothesis
$$54,000 : 3,000 (12 -x) = 2 : 1$$
or $$\cfrac{18}{12-x} = 2$$
or $$18 = 24-2x$$
or $$2x = 6$$
$$\therefore x = 3$$ months
Question 9
1 / -0

A certain sum of money lent out at S.I. amounts to Rs. 6900 in 3 years and Rs. 7500 in 5 years. The sum lent is

A
Rs. 4000

B
Rs. 4500

C
Rs. 5000

D
Rs. 6000

Solution

S.I. for 2 years $$= (7500 - 6900) = Rs. 600$$
S.I. for 3 years $$= Rs. (\cfrac{600}{2}\times 3)$$
$$= Rs. 900$$
$$\therefore$$ Principal $$= Rs. (6900 - 900)$$
$$= Rs. 6000$$
Question 10
1 / -0

A shopkeeper buys $$x$$ kg sugar for Rs. $$y$$ and sells it at Rs. $$z$$ per kg. Then expression for his profit can be represented by:

A
Profit = $$x - y + z$$

B
Profit = $$y - zx$$

C
Profit = $$x - zy$$

D
Profit = $$zx - y$$

Solution

Amount he sells $$x$$ kg of sugar = Rs. $$z$$ per kg.
$$\therefore S.P = Rs. zx$$ and $$C.P = Rs. y$$
$$\therefore Profit = zx - y $$

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Comparing Quantities Test - 23

Result

Comparing Quantities Test - 23

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SHARING IS CARING

Question 1

2%

5%

8%

10%

Solution

Question 2

65%

80%

85%

90%

Solution

Question 3

$$4 : 3$$

$$2 : 3$$

$$1 : 1$$

$$6 : 5$$

Solution

Question 4

8%

9%

10%

11%

Question 5

Rs. $$28$$

Rs. $$25$$

Rs. $$20$$

Rs. $$15$$

Solution

Question 6

Rs. 7.50 per kg

Rs. 9 per kg

Rs. 8.20 per kg

Rs. 8.85 per kg

Solution

Question 7

Loss of $$20\%$$

Loss of $$25\%$$

Gain of $$20\%$$`

Gain of $$25\%$$

Solution

Question 8

1 month

2 months

3 months

4 months

Solution

Question 9

Rs. 4000

Rs. 4500

Rs. 5000

Rs. 6000

Solution

Question 10

Profit = $$x - y + z$$

Profit = $$y - zx$$

Profit = $$x - zy$$

Profit = $$zx - y$$

Solution

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