Comparing Quantities Test

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Comparing Quantities Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. Find the sum.

A
Rs. $$698$$

B
Rs. $$798$$

C
Rs. $$658$$

D
Rs. $$758$$

Solution

$$\textbf{Step 1: Find the simple interest in one year and 3 years.}$$

$$\text{Given,}$$
$$\text{Sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years.}$$
$$\text{So, Amount after 4 years= Amount after 3 years }+\text{ Simple interest in 1 year} $$
$$\therefore \text{Simple interest in one year}=854-815$$
$$=\text{Rs. } 39$$
$$\text{Simple interest for 3 years}=39\times 3$$
$$=\text{Rs. }117$$

$$\textbf{Step 2: Find the principle value.}$$

$$\text{Principle}=815-117$$ $$[\because\textbf{Principle}=\textbf{Amount}-\textbf{Interest}]$$
$$=\text{Rs. }698$$

$$\textbf{Hence, Option A is correct.}$$
Question 2
1 / -0

Cost price for $$15$$ items is $$122.5$$ and selling price of $$12$$ items is $$108$$. Then, the number of articles sold to make a profit of Rs. $$75$$ is:

A
$$66$$

B
$$50$$

C
$$44$$

D
$$30$$

Solution

Cost price of $$15$$ articles is $$122.5$$ Rs
So, cost price of one article $$=\dfrac {112.50}{15}=\dfrac {22.5}{3} =$$ Rs. $$7.5 $$

Selling price of $$12$$ articles is Rs. $$108$$
So, selling price of one article $$ =$$ Rs. $$\dfrac {108}{12}=$$ Rs. $$9$$

Profit on one article $$=9 - 7.5=$$ Rs. $$1.5$$

Number of articles sold to make a profit of Rs. $$75 = \dfrac{75}{1.5}=50$$
Question 3
1 / -0

The ratio $$15:75$$ in its simplest form is

A
$$1:8$$

B
$$1:5$$

C
$$7:1$$

D
$$1:7$$

Solution

Given ratio is $$15:75$$

$$\Rightarrow \cfrac{15}{75} =\cfrac{1 \times15}{5 \times15}=\cfrac{1}{5}$$

so, the simplest form is $$1:5$$
Question 4
1 / -0

A shopkeeper bought 300 eggs at 80 paise each. 30 eggs were broken in the transaction and then sold the remaining eggs at one rupee each. Find his gain or loss as per cent.

A
12.5% gain

B
15.0% gain

C
12.5% loss

D
15.0% loss

Solution

Total money spent for 300 eggs $$ C.P. = Rs 0.80 \times 300 = Rs 240 $$

As only $$ 300 - 30 = 270 $$ eggs were sold, $$ => S.P. = Rs 1 \times 270 = Rs 270 $$

Since S.P. > C.P, there is a profit

Profit % $$ = \cfrac {S.P. -C.P. }{C.P} \times 100 = \cfrac { 270 - 240 }{ 240 } \times 100 = 12.5 $$ %
Question 5
1 / -0

The cost price of an article is Rs. 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.

A
Rs. $$120$$ and $$3.37$$%

B
Rs. $$130$$ and $$4.25$$%

C
Rs. $$140$$ and $$6$$%

D
Rs. $$150$$ and $$6.25$$%

Solution

Marked price will be $$ = C.P. +\; 25 $$ % of $$ C.P. = \dfrac {125}{100} \times C.P. = \dfrac {125}{100} \times 2400 =Rs\; 3000 $$

And Discount $$ = 15 $$ % of Marked Price $$ = \dfrac {15}{100} \times 3000 = Rs\;450 $$

And Selling price will be $$ = $$ Marked Price $$ - $$ Discount $$ = Rs\; 3000 - Rs\;450 = Rs\;2550 $$

Now, Gain $$ = S.P. - C.P. = Rs\;2550 - Rs\;2400 = Rs\;150 $$
Gain % $$ = \dfrac {S.P. - C.P.}{C.P.} \times 100 = \dfrac {2550 - 2400}{2400} \times 100 = 6.25 $$ %
Question 6
1 / -0

A man buys $$m$$ articles at Rs. $$x$$ each and another $$n$$ articles for Rs. $$y$$. If he sells all the articles at Rs. $$z$$ per article, frame an equation to find his profit

A
$$(mx + n) z - (mx + y)$$

B
$$(m + n) zx - (mx + y)$$

C
$$(m + n) z - (mx +n y)$$

D
$$(mn + x) z - (mx + y)$$

Solution

Cost price for a article is Rs $$x$$
Cost price of $$m$$ articles is Rs $$mx$$.
Cost price of another articles is Rs $$y$$
Cost price of $$n$$ another articles is Rs $$ny$$
Total cost price $$=$$ Rs $$ mx +ny$$
Selling price of a article is Rs $$z$$
Therefore Selling Price for $$(m+n)$$ articles $$=$$ $$z(m+n)$$
Profit $$=$$ Selling price $$-$$ Cost price
Profit $$= z(m+n) - (mx + ny)\\ $$
Question 7
1 / -0

If Rs.3,750 amount to Rs.4,620 in 3 years at simple interest, then find the rate of interest.

A
$$\displaystyle 7\frac{11}{15}$$%

B
$$\displaystyle 8\frac{11}{15}$$%

C
$$\displaystyle 6\frac{11}{15}$$%

D
$$\displaystyle 5\frac{11}{15}$$%

Solution

Simple Interest $$ I = \cfrac {PNR}{100} $$
Given,
Amount $$A = Rs. 4620 $$
$$ P = Rs. 3750 $$
$$ I = A - P = 870 $$
$$ N = 3$$

So, $$ 870 = \cfrac {3750 \times 3 \times R}{100} $$
$$ => R = 7 \cfrac {11}{15} \%$$
Question 8
1 / -0

A manufacturer makes a profit of 15% by selling a colour T.V. for Rs. 5,750. If the cost of manufacturing increases by 30 per cent and its selling price is increased by 20 per cent, find the profit per cent made by the manufacturer.

A
$$\displaystyle 2\frac{2}{13}$$%

B
$$\displaystyle 5\frac{2}{13}$$%

C
$$\displaystyle 6\frac{2}{13}$$%

D
$$\displaystyle 9\frac{2}{13}$$%

Solution

Given, for first TV
$$ S.P = Rs 5,750 $$
Profit $$ = 15 $$ %

Profit % $$ = \dfrac {S.P. - C.P.}{C.P.} \times 100$$
$$ = 15 $$ %

$$ \dfrac {5,750 - C.P.}{C.P.} \times 100 = 15 $$
$$ 5,750 - C.P. = 0.15 C.P. $$
$$ 1.15 C.P. = 5,750 $$
$$ => C.P. = Rs 5,000 $$

As per given information, for another TV
$$ C.P. = \dfrac {130}{100} \times Rs 5,000 = Rs 6500 $$
$$ S.P. = \dfrac {120}{100} \times Rs 5,750 = Rs 6900 $$

So, Profit % $$ = \dfrac {S.P. - C.P.}{C.P.} \times 100$$
$$ = \dfrac {6900-6500}{6500} \times 100$$
$$ =\dfrac {400}{6500} \times 100$$
$$ = \dfrac {400}{65}$$
$$ = \dfrac {80}{13}$$
$$ = 6 \dfrac {2}{13} $$ %
Question 9
1 / -0

If A merchant purchases 9 pens and sells 8 pens at the cost price of 9 pens, then his profit percent is:

A
5$$\displaystyle{\frac{15}{17}}$$

B
8$$\displaystyle{\frac{2}{3}}$$

C
12$$\displaystyle{\frac{1}{2}}$$

D
11$$\displaystyle{\frac{1}{9}}$$

Solution

Let CP of 1 pen $$= x$$
CP of 9 pen $$=$$ 9x and CP of 8 pen $$= 8x$$
According to the question
SP of 8 pens $$= 9x$$
% profit $$=$$ $$\displaystyle{\frac{9x - 8x}{8x} \times 100}$$
$$= \displaystyle{\frac{100}{8}}= 12\displaystyle{\frac{1}{2}}$$
Hence, option 'C' is correct.
Question 10
1 / -0

By selling tea for $$Rs \ 67.20$$ per kg, a profit of $$12\%$$ is made, find profit made by selling $$8$$ kg tea.

A
$$Rs$$ $$57.60$$

B
$$Rs$$ $$67.60$$

C
$$Rs$$ $$52.60$$

D
none of these

Solution

Given, Profit % by selling 1 kg of tea $$ = \frac {S.P - C.P.}{C.P.} \times 100 = 12 $$ %
$$ \implies \frac {67.20- C.P.}{C.P.} \times 100 = 12 $$
$$ \implies 67.20- C.P. = 0.12 C.P. $$
$$\implies 1.12 C.P. = 67.20 $$
$$ C.P. = Rs 60 $$

So, C.P. of $$ 8 $$ kg tea $$ = Rs 8 \times 60 = Rs 480 $$
S.P. of $$ 8 $$ kg tea $$ = Rs 8 \times 67.20 = Rs 537.6 $$

$$ \implies Profit = SP -CP = Rs 537.6 - Rs 480 = Rs 57.60 $$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 24

Result

Comparing Quantities Test - 24

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SHARING IS CARING

Question 1

Rs. $$698$$

Rs. $$798$$

Rs. $$658$$

Rs. $$758$$

Solution

Question 2

$$66$$

$$50$$

$$44$$

$$30$$

Solution

Question 3

$$1:8$$

$$1:5$$

$$7:1$$

$$1:7$$

Solution

Question 4

12.5% gain

15.0% gain

12.5% loss

15.0% loss

Solution

Question 5

Rs. $$120$$ and $$3.37$$%

Rs. $$130$$ and $$4.25$$%

Rs. $$140$$ and $$6$$%

Rs. $$150$$ and $$6.25$$%

Solution

Question 6

$$(mx + n) z - (mx + y)$$

$$(m + n) zx - (mx + y)$$

$$(m + n) z - (mx +n y)$$

$$(mn + x) z - (mx + y)$$

Solution

Question 7

$$\displaystyle 7\frac{11}{15}$$%

$$\displaystyle 8\frac{11}{15}$$%

$$\displaystyle 6\frac{11}{15}$$%

$$\displaystyle 5\frac{11}{15}$$%

Solution

Question 8

$$\displaystyle 2\frac{2}{13}$$%

$$\displaystyle 5\frac{2}{13}$$%

$$\displaystyle 6\frac{2}{13}$$%

$$\displaystyle 9\frac{2}{13}$$%

Solution

Question 9

5$$\displaystyle{\frac{15}{17}}$$

8$$\displaystyle{\frac{2}{3}}$$

12$$\displaystyle{\frac{1}{2}}$$

11$$\displaystyle{\frac{1}{9}}$$

Solution

Question 10

$$Rs$$ $$57.60$$

$$Rs$$ $$67.60$$

$$Rs$$ $$52.60$$

none of these

Solution

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