Comparing Quantities Test

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Comparing Quantities Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

Mark again the correct answer in each of the following:
$$(3/4)$$ as rate percent is

A
$$7.5\%$$

B
$$75\%$$

C
$$0.75\%$$

D
None of these

Solution

Because,
$$=(3/4)\times 100$$
$$=(300/4)$$
$$=75\%$$
Question 2
1 / -0

The per cent that represents the unshaded region in the figure.

A
$$75\%$$

B
$$50\%$$

C
$$40\%$$

D
$$60\%$$

Solution

By counting ,
Unshaded parts $$= 40$$
Total parts $$= 100$$
Unshaded fraction $$=\dfrac{\text {unshaded parts}}{\text{total parts}}= \dfrac{40}{100} = 40\%$$
Question 3
1 / -0

A man loses $$12\frac{1}{2} $$ % of his money and after spending 70% of the remainder, he was left with Rs. 210. The money that he had at the beginning is

A
Rs. 810

B
Rs. 800

C
Rs. 790

D
Rs. 780

Solution

Let Rs. $$x$$ be the amount at the beginning.
Loss $$ = 12.5\%$$
Remainder $$ = \cfrac{87.5x}{100}$$

$$210 = \cfrac{30}{100} \times \dfrac{87.5x}{100}$$

$$\therefore x=800$$
Question 4
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 5
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 6
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 7
1 / -0

A certain sum of money Q was deposited for 5 years and 4 months at 4.5% simple interest and mounted to Rs. 248. Then the value of Q is

A
Rs. 200

B
Rs. 210

C
Rs. 220

D
Rs. 240

Solution

We know that,
Amount = principle + simple interest
$$A=P+\cfrac{PRT}{100}$$
$$A=P[1+\cfrac{RT}{100}]$$            ...... (1)
Where, $$A$$ is amount.
            $$P$$ is principle.
            $$R$$ is rate of interest.
            $$T$$ is time in year.

Given, $$A=248$$
            $$P=Q$$
            $$R=4.5$$%
            $$T=5+\cfrac{4}{12}=\cfrac{16}{3}$$
Substitute these values in equation (1) and find the value of $$Q$$.
$$248=Q[1+\cfrac{4.5\times\frac{16}{3}}{100}]$$
$$248=Q[1+\cfrac{24}{100}]$$
$$248=1.24Q$$
$$\therefore Q=200$$
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

A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction.

A
$$2$$% Profit

B
$$1 $$% Profit

C
$$3 $$ % loss

D
$$4 $$ % loss

Solution

Cost Price (CP) of VCR is Rs $$8000$$

Cost Price (CP) of TV is Rs $$8000$$

Total CP$$=$$Rs $$16,000$$

Loss on$$ VCR=CP\times Loss$$%

$$=8000\times\dfrac{4}{100}$$

$$=320$$

Profit on $$TV=CP\times Profit$$%

$$=8000\times\dfrac{8}{100}$$

$$=640$$

Total profit$$=640-320$$

$$=320$$

Percentage profit $$=\dfrac{profit}{CP}\times100$$

$$=\dfrac{320}{16000}\times100$$

$$=2$$%
Question 10
1 / -0

Rakesh took a loan for 7 years at the rate of 6% p.a. S.I. If the total interest paid was Rs. 2100, the principal was

A
Rs. 4400

B
Rs. 4800

C
Rs. 5000

D
Rs. 5200

Solution

Given that,
Rakesh took a loan for $$7$$ years at $$6\%$$ per annum simple interest.
He paide $$Rs.\ 2100$$ interest on the amount.

To find out,
The principal amount.

We know that, $$S.I.=\left(\dfrac{P\times R\times T}{100}\right)$$

Here, $$S.I.=Rs.\ 2100,\ R=6\%$$ and $$T=7\ years$$

Hence, $$2100=\left(\dfrac{P\times 6\times 7}{100}\right)$$

$$\Rightarrow P=\left(\dfrac{2100\times 100}{6\times 7}\right)$$

$$\Rightarrow P=\left(\dfrac{2100\times 100}{42}\right)$$

$$\Rightarrow P=50\times 100$$

$$\therefore\ P=Rs.\ 5000$$

Hence, the principal amount was $$Rs.\ 5000$$.

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 22

Result

Comparing Quantities Test - 22

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SHARING IS CARING

Question 1

$$7.5\%$$

$$75\%$$

$$0.75\%$$

None of these

Solution

Question 2

$$75\%$$

$$50\%$$

$$40\%$$

$$60\%$$

Solution

Question 3

Rs. 810

Rs. 800

Rs. 790

Rs. 780

Solution

Question 4

$$Rs. 2.20$$

$$Rs. 2.00$$

$$Rs.2.35$$

$$Rs. 2.40$$

Solution

Question 5

$$350\ \text{kg}$$

$$300\ \text{kg}$$

$$250\ \text{kg}$$

$$325\ \text{kg}$$

Solution

Question 6

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

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

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

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

Solution

Question 7

Rs. 200

Rs. 210

Rs. 220

Rs. 240

Solution

Question 8

5 months

7 months

8 months

9 months

Solution

Question 9

$$2$$% Profit

$$1 $$% Profit

$$3 $$ % loss

$$4 $$ % loss

Solution

Question 10

Rs. 4400

Rs. 4800

Rs. 5000

Rs. 5200

Solution

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