Comparing Quantities Test

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Comparing Quantities Test - 58

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Question 1
1 / -0

The cost price of an article is $$x$$. It is marked up by $$150$$%. It is sold at Rs. $$600$$ after giving $$40$$% discount. What is $$x$$ (in Rs.)?

A
$$494.44$$

B
$$666.66$$

C
$$840$$

D
$$942$$

Solution

Given that, the cost price of an article is $$Rs.\ x$$. It is marked up by $$150\%$$ and sold at $$Rs.\ 600$$ after a discount of $$40\%$$.
To find out: The value of $$x$$.

$$C.P.=Rs.\ x$$
Hence, marked price $$(M.P.)=150\% \ of\ x=Rs.\ 1.5x$$
We know that,
$$S.P.=\dfrac{100-\%\text{discount}}{100}\times M.P.$$

$$\therefore \ 600=\dfrac{100-40}{100}\times 1.5x$$

$$\Rightarrow \ 600=\dfrac{6}{10}\times 1.5x$$

$$\Rightarrow \ 1.5x=1000$$

$$\Rightarrow \ x=\dfrac{1000}{1.5}=\dfrac{10000}{15}$$

$$\therefore \ x=666.66$$

Hence, the cost price of the article $$(x)$$ is $$Rs.\ 666.66$$.
Question 2
1 / -0

Mr,A owns a home worth Rs.$$10,000$$. He sells it to Mr.B at a $$10\%$$ profit based on the worth of the house. Mr.B sells the house back to Mr.A at a $$10\%$$ loss. Then:

A
A comes out even

B
A makes Rs.$$1100$$ on the deal

C
A makes Rs.$$1000$$ on the deal

D
A loses Rs.$$900$$ on the deal

Solution

$$\text{C.P. of B = 110% of Rs. 10000 = Rs. 11000}$$
$$\text{Loss of B = 10%}$$
$$\text{S.P. of B = 90% of Rs. 11000 = Rs. 9900}$$
$$\text{Thus, C.P. of A = Rs. 9900}$$
$$\text{So, A gets [(10% of Rs. 10000) + (10000 - 9900)] = Rs. 1100}$$
Question 3
1 / -0

$$5$$% more is gained by selling a watch for $$Rs. 350$$ than by selling it for $$Rs. 340$$. The cost price of the watch is

A
$$Rs. 110$$

B
$$Rs. 140$$

C
$$Rs. 200$$

D
$$Rs. 250$$

Solution

Let cost price be $$Rs. x$$
Then $$5$$% of $$x = (350 - 340)$$
$$5$$% of $$x = 10$$
$$x = 10\times \dfrac {100}{5} = 200$$
Hence, cost price is $$Rs. 200$$.
Question 4
1 / -0

Find the whole quantity if $$5\%$$ of it is $$600$$.

A
$$3000$$

B
$$6000$$

C
$$12000$$

D
$$15000$$

Solution

Given $$\dfrac{5}{100}$$ of $$x=600$$

$$\implies x=\dfrac{600\times 100}{5}= Rs$$ $$12000$$
Question 5
1 / -0

A house and store were sold for $$\text{Rs. } 12,000$$ each. The house was sold at a loss of $$20\%$$ of the cost and the store at a gain of $$20\%$$ of the cost. The entire transaction resulted in

A
No loss or gain

B
Loss of $$\text{Rs. } 1000$$

C
Gain of $$\text{Rs. } 1000$$

D
Gain of $$\text{Rs. } 2000$$

E
None of these

Solution

$$12,000 = H - \dfrac {1}{5}H \therefore H = 15,000$$
$$12,000 = S + \dfrac {1}{5}S \therefore S = 10,000$$
$$ H + S = 25,000$$.
Therefore, the sale resulted in a loss of $$Rs. 1000$$.
Question 6
1 / -0

The cost $$C$$ of sending a parcel post package weighing $$P$$ gms, $$P$$ an integer is $$Rs. 10$$ for the first grams and $$Rs. 3$$ for each additional grams. The formula for the cost is

A
$$C = 10 + 3P$$

B
$$C = 10P + 3$$

C
$$C = 10 + 3 (P - 1)$$

D
$$C = 9 + 3P$$

E
$$C = 10P - 7$$

Solution

For $$P - 1$$ gms the charge is $$3$$ rupees per grams. For the first gram the charge is $$10$$ rupees. $$\therefore C = 10 + 3(P - 1)$$; or
The charge for each gram is $$3$$ rupees with an additional charge of $$7$$ rupees for the first gram. $$\therefore C = 3P + 7 = 3P - 3 + 10 = 10 + 3(P - 1)$$.
Question 7
1 / -0

A shopkeeper allows a discount of $$10\%$$ on the marked price of an item but charges a sales tax of $$8\%$$ on the discounted price. If the customer pays $$Rs.680.40$$ as the price including the sales tax, then what is the marked price of the item?

A
Rs. $$630$$

B
Rs. $$700$$

C
Rs. $$780$$

D
Rs. $$680$$

Solution

Let marked price be $$Rs.x$$
Price after discount of $$10\%=x-x\times \dfrac{10}{100}=\dfrac{9x}{10}$$

Price after Tax $$=\dfrac{9x}{10}+\left(\dfrac{9x}{10}\times \dfrac{8}{100} \right)=\dfrac{972x}{1000}$$

It is given that:

$$\Rightarrow$$ $$\dfrac{972x}{1000}=680.40$$

$$\Rightarrow$$ $$x=\dfrac{680400}{972}$$

$$\therefore$$ $$x=Rs.700.$$

$$\therefore$$ Marked price of the item is $$Rs.700$$
Question 8
1 / -0

A wholesaler bought $$120$$ watches for $$\text{Rs }30$$ each. He sold $$50\%$$ of the watches for $$\text{Rs }20$$ each, one-third at $$\text{Rs }40$$ each and the rest for $$\text{Rs }60$$. What was the wholesaler's approximate avenge profit per watch?

A
$$\text{Rs }3.3$$

B
$$\text{Rs }5$$

C
$$\text{Rs }7$$

D
$$\text{Rs }9$$

E
$$\text{Rs }11$$

Solution

C.P. of each watch $$=\text{Rs }30$$ , number of watches $$=120$$
total C.P. $$=30\times 120=\text{Rs }3600$$
Wholesaler sold $$50\%$$ ($$60$$ watches) at $$\text{Rs }20$$
S.P. of these $$60$$ watches $$(S.P_1)=60 \times 20=\text{Rs }1200=$$
$$\left(\dfrac{1}{3}\right)^{rd}$$ of $$120$$ watches are sold at $$\text{Rs }40$$
$$S.P_2=40\times 40=\text{Rs }1600$$
rest $$(120-60-40=20)$$ watches are sold at $$\text{Rs }60$$
$$S.P_3=20\times 60=\text{Rs }1200$$
Total S.P. $$=1200+1600+1200=\text{Rs }4000$$
profit $$=$$ S.P. $$-$$ C.P. $$=4000-3600=\text{Rs }400$$
Average profit per watch $$=\dfrac{400}{120}=\text{Rs }3.3$$
Question 9
1 / -0

A trader allows successive discounts of $$15\%$$ and $$10\%$$ on the marked price of an article. If the marked price is $$Rs. 100$$, what would be the selling price?

A
$$Rs.\ 76.50$$

B
$$Rs.\ 75$$

C
$$Rs.\ 80$$

D
$$Rs.\ 77$$

Solution

Marked Price $$= Rs\ 100$$

Price after $$15\%$$ discount:

$$15\%$$ Discount $$= 0.15 x 100 = Rs\ 15$$

Price after discount $$= 100 - 15 = Rs\ 85$$

Price after $$10\%$$ discount:

$$10\%$$ Discount $$= 0.10 x 85 = Rs\ 8.50$$

Price after discount $$= 85 - 8.5 = Rs\ 76.50$$

Hence, the selling price is $$Rs\ 76.50$$
Question 10
1 / -0

A TV was bought at a price of Rs. 21,000. After one year the value of the TV was depreciated by 5%. (Depreciation means reduction of value due to use and age of the item). Find the value of the TV after one year.

A
19,750

B
17,950

C
19,950

D
19,000

Solution

$$\textbf{Step -1:Calculate the value to be deduced}.$$
$$\text{We are given that after one year, the value of the TV is depreciated by}$$ $$5\%.$$
$$\text{Value to be deduced =}$$$$5$$$$\text{% of}$$ $$Rs.21,000$$
$$=Rs.\dfrac{21000\times 5}{100}$$
$$=Rs.\: 1050$$
$$\textbf{Step -2:Calculate the value of the TV after one year}.$$
$$\text{Value after one year=}$$$$Rs.(21000-1050)$$
$$=Rs.\: 19,950$$

$$\textbf{Hence, the correct option is C.}$$

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Comparing Quantities Test - 58

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Comparing Quantities Test - 58

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Question 1

$$494.44$$

$$666.66$$

$$840$$

$$942$$

Solution

Question 2

A comes out even

A makes Rs.$$1100$$ on the deal

A makes Rs.$$1000$$ on the deal

A loses Rs.$$900$$ on the deal

Solution

Question 3

$$Rs. 110$$

$$Rs. 140$$

$$Rs. 200$$

$$Rs. 250$$

Solution

Question 4

$$3000$$

$$6000$$

$$12000$$

$$15000$$

Solution

Question 5

No loss or gain

Loss of $$\text{Rs. } 1000$$

Gain of $$\text{Rs. } 1000$$

Gain of $$\text{Rs. } 2000$$

None of these

Solution

Question 6

$$C = 10 + 3P$$

$$C = 10P + 3$$

$$C = 10 + 3 (P - 1)$$

$$C = 9 + 3P$$

$$C = 10P - 7$$

Solution

Question 7

Rs. $$630$$

Rs. $$700$$

Rs. $$780$$

Rs. $$680$$

Solution

Question 8

$$\text{Rs }3.3$$

$$\text{Rs }5$$

$$\text{Rs }7$$

$$\text{Rs }9$$

$$\text{Rs }11$$

Solution

Question 9

$$Rs.\ 76.50$$

$$Rs.\ 75$$

$$Rs.\ 80$$

$$Rs.\ 77$$

Solution

Question 10

19,750

17,950

19,950

19,000

Solution

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