Comparing Quantities Test

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Comparing Quantities Test - 42

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Weekly Quiz Competition

Question 1
1 / -0

A man bought at the cost of $$5$$ plums a rupee and $$2$$ oranges a rupee. He sells $$10$$ plums and $$6$$ oranges at the selling price of $$4$$ plums a rupee and $$3$$ oranges a rupee. What is his gain or loss?

A
Gain $$50$$ paise

B
Loss $$50$$ paise

C
Gain $$30$$ paise

D
Loss $$30$$ paise

Solution

Cost price of $$1$$ plum $$= \dfrac {100}{5} = 20$$ paise
Cost price of $$10$$ plum $$= 20 \times 10 = 200$$ paise
Cost price of $$1$$ orange $$= \dfrac {100}{2} = 50$$ paise
Cost price of $$6$$ oranges $$= 50 \times 6 = 300$$ paise
Selling price per plums $$=\dfrac { 100 }{ 4} = 25$$ paise
So, selling price of $$10$$ plums $$= 25 \times 10 = 250$$ paise
Selling price of $$6$$ oranges $$= 200$$ paise
Total cost price $$= 200 + 300 = 500$$ paise
Total selling price $$= 250 + 200 = 450$$ paise
So, loss $$= 500 - 450 = 50$$ paise.
Question 2
1 / -0

An article is sold at $$10\%$$ profit . If its cost price and selling price are $$50$$ less, the profit would be $$5\%$$ more. Find the cost price?

A
$$40$$

B
$$45$$

C
$$60$$

D
$$120$$

E
$$150$$

Solution

$$let,\,C.P=x$$
and $$gain\%=10\%$$
$$S.P=\left(\dfrac{100+gain}{100}\right)\times C.P\Rightarrow S.P=\dfrac{110x}{100}$$

$$new \,C.P=C.P-50$$
$$new \,S.P=S.P-50$$
$$gain\%=5\%\,more \,than\,previous=15\%$$
$$\Rightarrow New\,S.P=\left(\dfrac{100+gain}{100}\right)\times(New\,C.P)$$
$$\Rightarrow (S.P-50)=\left(\dfrac{100+15}{100}\right)\times(C.P-50)$$
$$\Rightarrow (\dfrac{110x}{100}\,-\,50)=\dfrac{115}{100}\times (x-50)$$
$$\Rightarrow \dfrac{110x}{100}\,-50=\dfrac{115x}{100}-\dfrac{115}{2}$$
$$\Rightarrow \dfrac{115}{2}\,-\,\dfrac{100}{2}=\dfrac{115x}{100}-\dfrac{110x}{100}$$
$$\Rightarrow \dfrac{15}{2}=\dfrac{5x}{100}$$
$$\therefore x=150$$
Question 3
1 / -0

A and B invest in a business in the ratio of $$3 : 2$$. If $$5$$ % of total profit goes to charity and A's share is Rs. $$8550$$, then total profit is :

A
Rs. $$14000$$

B
Rs. $$15000$$

C
Rs. $$16000$$

D
Rs. $$16500$$

Solution

Let Total Profit is Rs. 100
After 5 % charity, profit = Rs 95
So, share of A = (95 *3)/5 = Rs. 57
Now, comparing,
A share $$57$$ on profit $$100$$
So, A's share 1 on profit $$= 100/57$$
Thus, A shares Rs. $$8550$$ on =$$ (8550 *100)/57 = Rs. 15000$$
Question 4
1 / -0

A manufacturer undertakes to supply $$2000$$ pieces of particular component at Rs. $$25$$ per piece. According to his estimates, even if $$5\%$$ fail to pass the quality tests, then he will make a profit of $$25\%$$. However, as it turned out, $$50\%$$ of the components were rejected . what is the loss to the manufacturer ?

A
Rs. $$12,000$$

B
Rs. $$13,000$$

C
Rs. $$14,000$$

D
Rs. $$15,000$$

Solution

Total number of component $$= 2000$$
If $$15\%$$ component found to be defective
Then, number of non-defective component $$= 2000 - 5\% $$ of $$ 2000 =2000-\dfrac{5}{100}\times 2000= 1900$$

So, selling price of $$190$$ component $$= 1900 \times 25 =$$ Rs. $$47500$$

This content $$25\%$$ profit of the manufacturer.

Let the total manufacturing price of the component $$ = x$$

SP$$ = 47500$$

$$\Rightarrow x + 25\% $$ of $$ x = 47500$$

$$\Rightarrow \dfrac{ 100x + 25x }{100 }= 47500$$

$$\Rightarrow 125 x = 4750000$$

$$\Rightarrow x =$$ Rs. $$38000$$

If $$50$$ component i.e. $$1000$$ components are defective. then

Total collection $$= 25 \times 1000 = 25000$$

Loss $$ = 38000 - 25000 =$$ Rs. $$13000$$
Question 5
1 / -0

The profit after selling a pair of trousers for Rs. $$863$$ is the same as the loss incurred after selling the same pair of trousers for Rs. $$631$$. What is the cost price of the pair of trousers?

A
$$750$$

B
$$800$$

C
$$763$$

D
$$864$$

E
None of these

Solution

Let the C.P. be $$x$$.
Then, Profit $$= 863 - x$$
Loss $$= x - 631$$
Given, profit $$=$$ Loss
$$\Rightarrow 863 - x = x - 631$$
$$\Rightarrow 2x = 863+631 = 1494$$
$$\Rightarrow x = \dfrac {1494}{2} = 747$$
Cost Price $$=$$ Rs. $$747$$
Question 6
1 / -0

A man sold $$18$$ toys for Rs. $$16800$$, gaining thereby the cost price of $$3$$ toy. find the cost price of a toy.

A
Rs. $$ 600$$

B
Rs. $$ 800$$

C
Rs. $$ 500$$

D
Rs. $$ 900$$

Solution

Let the cost of one toy be $$ x$$
Then, cost of $$18$$ toy $$= 18x$$
Gain $$ = 3x $$
SP of $$18$$ toys $$ =$$ Rs. $$16800$$
Gain $$=$$ S.P. $$-$$ C.P.
$$\Rightarrow 3x = 16800 - 18x$$
$$\Rightarrow 21x = 16800$$
$$\Rightarrow x = \dfrac{16800}{21}=$$ Rs. $$ 800$$
Therefore, cost price of a toy is Rs. $$800$$.
Question 7
1 / -0

A sells a bicycle to $$B$$ at a profit of $$20\%$$. $$B$$ sells it to $$C$$ at a profit of $$25\%$$. If $$C$$ pays Rs. $$225$$ for it, the cost price of the bicycle for $$A$$ is

A
Rs. $$110$$

B
Rs. $$120$$

C
Rs. $$125$$

D
Rs. $$150$$

Solution

Let the C.P for $$A=$$ Rs. $$ x$$
Profit $$=20\%$$
Then S.P for $$A$$ $$=\dfrac{120}{100}\times x=$$ Rs. $$\dfrac{12x}{10}$$
S.P. for $$A=$$ C.P. for $$B$$ $$=$$ Rs. $$\dfrac{12x}{10}$$
Profit $$=25\%$$
then S.P for $$B$$ $$=\dfrac{25}{100}\times \dfrac{12x}{10}=$$ Rs. $$\dfrac{3x}{2}$$
S.P. for $$B =$$ C.P. for $$C=$$ Rs. $$\dfrac{3x}{2}$$
According to the question,
C.P for $$C=$$ Rs. $$225$$
$$\therefore \dfrac{3x}{2}=225$$
$$\Rightarrow x=\dfrac{225\times 2}{3}=$$ Rs. $$150$$
Hence, cost of the bicycle for $$A$$ is Rs. $$150$$.
Question 8
1 / -0

The prices of two articles are in the ratio of $$3 : 4$$. If the price of the first article be increased by $$10$$% and that of the second by Rs $$4$$, the original ratio remains the same. The original price of second article is ?

A
Rs $$30$$

B
Rs $$35$$

C
Rs $$40$$

D
Rs $$45$$

Solution

Let price of two articles are $$3x$$ and $$4x$$
After increment price become $$3.3x$$ and $$(4x + 4)$$
Now, according to question,
$$\dfrac{3.3x}{(4x + 4)} = \dfrac{3}{4}$$
$$13.2x = 12x + 1$$
$$13.2x - 12x = 12$$
$$1.2x = 12$$
$$x = 10$$
So, original price of second article $$= 4x = 4 \times10 = $$Rs $$40$$.
Question 9
1 / -0

Jacob bought a scooter for a certain sum of money. He spent $$10\%$$ of the cost on repairs and sold the scooter for a profit of Rs. $$1100$$. How much did he spend on repairs if he made a profit of $$20\%$$.

A
Rs. $$400$$

B
Rs. $$440$$

C
Rs. $$500$$

D
Rs. $$550$$

Solution

Total profit $$=$$ Rs. $$1100$$
Percent profit $$= 20$$
$$\Rightarrow 20\% = 1100$$
So, $$100\%=5500$$
Rs. $$5500$$ would be the cost price for Jacob.
He spends $$10\%$$ on repairing. so, the cost price was Rs. $$5000$$.
Thus, he spends Rs. $$500$$ on repairing.
Question 10
1 / -0

A shopkeeper bought 2 dozen of apples at RS. 58 and 4 dozen of oranges at Rs. 48. He sold the oranges to ram at 5% loss and apples to shyam at 15 % gain. What is overall loss or gain percentage in the transaction?

A
$$4.1$$

B
$$4.05$$

C
$$4.3$$

D
$$4.0$$

Solution

$$\text{CP of 2 dozen of apples}=Rs.\ 58$$
$$Loss=5\%$$
$$SP=58-0.05\times 58=Rs.\ 55.1$$

$$\text{CP of 4 dozen of oranges}=Rs.\ 48$$
$$Gain=15\%$$
$$SP=48+0.15\times 48=Rs.\ 55.2$$

Total cost price $$=48+58=Rs.\ 106$$
Total selling price $$=55.1+55.2=Rs.\ 110.3$$
Hence, $$SP>CP$$.
So, profit $$=110.3-106=Rs.\ 4.3$$
$$P(\%)=\dfrac{4.3}{106}\times 100=4.05\% $$

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 42

Result

Comparing Quantities Test - 42

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SHARING IS CARING

Question 1

Gain $$50$$ paise

Loss $$50$$ paise

Gain $$30$$ paise

Loss $$30$$ paise

Solution

Question 2

$$40$$

$$45$$

$$60$$

$$120$$

$$150$$

Solution

Question 3

Rs. $$14000$$

Rs. $$15000$$

Rs. $$16000$$

Rs. $$16500$$

Solution

Question 4

Rs. $$12,000$$

Rs. $$13,000$$

Rs. $$14,000$$

Rs. $$15,000$$

Solution

Question 5

$$750$$

$$800$$

$$763$$

$$864$$

None of these

Solution

Question 6

Rs. $$ 600$$

Rs. $$ 800$$

Rs. $$ 500$$

Rs. $$ 900$$

Solution

Question 7

Rs. $$110$$

Rs. $$120$$

Rs. $$125$$

Rs. $$150$$

Solution

Question 8

Rs $$30$$

Rs $$35$$

Rs $$40$$

Rs $$45$$

Solution

Question 9

Rs. $$400$$

Rs. $$440$$

Rs. $$500$$

Rs. $$550$$

Solution

Question 10

$$4.1$$

$$4.05$$

$$4.3$$

$$4.0$$

Solution

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