Comparing Quantities Test

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Comparing Quantities Test - 24

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Question 1
1 / -0

A person purchases $$20$$ litres of juice at $$Rs. 2.20$$ per litre and diluted it with water to make the contents $$22$$ litres. In order to earn $$10\%$$ profit he should sell the juice at

A
$$Rs. 2.20$$

B
$$Rs. 2.00$$

C
$$Rs.2.35$$

D
$$Rs. 2.40$$

Solution

Volume of juice purchased $$= 20$$ litres
Rate at which juice purchased $$= Rs.2.20$$ per litre

$$\Rightarrow$$ Cost price of juice $$= 20 \times 2.2 = Rs..44$$
In order to gain $$10\%$$ profit,
Selling price $$= \dfrac{110}{100} \times 44 = 48.4$$

Final volume of juice after dilution $$= 22$$ litres
$$\therefore$$ Rate of selling $$= \dfrac{48.4}{22} = Rs. 2.20$$
Question 2
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 3
1 / -0

How many $$\text{kg}$$ of sugar costing $$\text{Rs.}\ 5.75$$ per $$\text{kg}$$ should be mixed with $$75\ \text{kg}$$ of cheaper sugar costing $$\text{Rs.}\ 4.50$$ per $$\text{kg}$$ so that the mixture is worth $$\text{Rs.}\ 5.50$$ per $$\text{kg}$$ ?

A
$$350\ \text{kg}$$

B
$$300\ \text{kg}$$

C
$$250\ \text{kg}$$

D
$$325\ \text{kg}$$

Solution

Let say $$x\ \text{kg}$$ sugar costing $$\text{Rs.}\ 5.75$$ per $$\text{kg}$$ is added.

Total cost $$= \text{Rs.}\ (5.75x + 75) \times 4.50$$
$$=\text{Rs.}\ (5.75x+337.5)$$
Total sugar $$= (x + 75)\ \text{kg}$$

Average cost of sugar mixture $$=\dfrac{\text{Total cost of sugar}}{\text{Total sugar}}$$

$$5.5 = \dfrac{\left(5.75x + 337.5\right)}{\left(x + 75\right)}$$

$$5.5x + 412.5 = 5.75x + 337.5$$

$$75 = 0.25x$$

$$x =\dfrac{75}{0.25}$$

$$\therefore\,x = 300\ \text{kg}$$
Question 4
1 / -0

The list price of a parker pen is Rs. 160 and a customer buys it for Rs. 122.40 after two successive discounts. If first is 10%, then the second is

A
18%

B
17%

C
16%

D
15%

Solution

$$\Rightarrow$$ The list price of parker pen is $$Rs.160$$
$$\Rightarrow$$ Selling price of parker pen is $$Rs.122.40$$
$$\Rightarrow$$ Total discount = $$Rs.160-Rs.122.40=Rs.37.60$$
$$\Rightarrow$$ Fist discount is $$10\%$$ on list price
$$\therefore$$ Fist discount = $$\dfrac{10}{100}\times 160=Rs.16$$
$$\Rightarrow$$ Second discount = $$Rs.37.60-Rs.16=Rs.21.60$$
$$\Rightarrow$$ Pen price after 1st discount = $$Rs.160-Rs.16=Rs.144$$
$$\Rightarrow$$ Second discount $$\%$$ = $$\dfrac{21.60}{144}\times 100=15\%$$
Question 5
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 6
1 / -0

If the marked price of an article is Rs. x, and the selling price is Rs. y, then what is the discount percentage?

A
$$\frac{(x-y)100}{x}$$

B
$$\frac{(y-x)100}{x}$$

C
$$(\frac{y-x}{y})100$$

D
$$\frac{x-y}{100}$$
Question 7
1 / -0

A shopkeeper professes to sell the goods at cost price, but he uses a weight of 900 grams for a Kilogram. Then his gain percent is

A
$$\dfrac{100}{9}$$ %

B
$$\dfrac{100}{8}$$ %

C
$$\dfrac{100}{7}$$ %

D
$$\dfrac{100}{6}$$ %

Solution

Shopkeeper uses weight of 900 grams for a kilogram or 1000 grams.
$$\Rightarrow$$ $$\text{Profit} = 1000-900=100$$
$$\text{Profit}\ \%=\dfrac{100}{900}\times 100=\dfrac{100}{9}\%$$
Question 8
1 / -0

A began business with Rs. 4,500 and was joined afterward by B with Rs. 5,400. If the profit at the end of the year was divided in the ratio of 2:1, then the time of joining B was after:

A
5 months

B
7 months

C
8 months

D
9 months

Solution

$$\Rightarrow$$ Let B remained in the business for $$x$$ months. Then,
$$\Rightarrow$$ $$\dfrac{A}{B}=\dfrac{4500\times 12}{5400\times x}=\dfrac{54000}{5400x}=\dfrac{10}{x}$$

$$\therefore$$ $$\dfrac{10}{x}=\dfrac{2}{1}$$

$$\Rightarrow$$ $$2x=10$$
$$\therefore$$ $$x=5$$
$$\Rightarrow$$ Thus, B remained in the business for 5 months.
$$\Rightarrow$$ So, B joined the business after $$7\, months.$$
Question 9
1 / -0

The population of a small town is increased by $$\cfrac{15}{2}$$ % per annum for two years. If the present population is $$73, 960$$, then two years before the population was

A
$$68,000$$

B
$$70,000$$

C
$$64,000$$

D
$$60,000$$

Solution

$$A=P(1+\cfrac{R}{100})^n$$
$$73960=P(1+0.075)^2$$
$$\therefore P=64000$$
Question 10
1 / -0

During a sale, a shop offered a discount of $$10\%$$ on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs $$1450$$ and two shirts marked at Rs $$850$$ each

A
Rs $$2835$$

B
Rs $$3000$$

C
Rs $$2830$$

D
Rs $$2800$$

Solution

Given Marked Price of Jeans = Rs 1,450
Market Price of two Shirts= Rs 1,700

Total Price of a pair of jeans and two shirts $$=1450+2\times 850=3150$$
Now,
Discount = Marked Price x % Discount

$$=3150\times \dfrac { 10 }{ 100 } $$

$$=315$$

$$\therefore$$ Effective Price After Discount = Rs. $$\left( 3150-315 \right) =$$ Rs. $$2,835$$

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Comparing Quantities Test - 24

Result

Comparing Quantities Test - 24

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SHARING IS CARING

Question 1

$$Rs. 2.20$$

$$Rs. 2.00$$

$$Rs.2.35$$

$$Rs. 2.40$$

Solution

Question 2

$$4 : 3$$

$$2 : 3$$

$$1 : 1$$

$$6 : 5$$

Solution

Question 3

$$350\ \text{kg}$$

$$300\ \text{kg}$$

$$250\ \text{kg}$$

$$325\ \text{kg}$$

Solution

Question 4

18%

17%

16%

15%

Solution

Question 5

65%

80%

85%

90%

Solution

Question 6

$$\frac{(x-y)100}{x}$$

$$\frac{(y-x)100}{x}$$

$$(\frac{y-x}{y})100$$

$$\frac{x-y}{100}$$

Question 7

$$\dfrac{100}{9}$$ %

$$\dfrac{100}{8}$$ %

$$\dfrac{100}{7}$$ %

$$\dfrac{100}{6}$$ %

Solution

Question 8

5 months

7 months

8 months

9 months

Solution

Question 9

$$68,000$$

$$70,000$$

$$64,000$$

$$60,000$$

Solution

Question 10

Rs $$2835$$

Rs $$3000$$

Rs $$2830$$

Rs $$2800$$

Solution

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