Comparing Quantities Test

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Comparing Quantities Test - 58

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Weekly Quiz Competition

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

494.44494.44494.44

666.66666.66666.66

840840840

942942942

Solution

Question 2

A comes out even

A makes Rs.110011001100 on the deal

A makes Rs.100010001000 on the deal

A loses Rs.900900900 on the deal

Solution

Question 3

Rs.110Rs. 110Rs.110

Rs.140Rs. 140Rs.140

Rs.200Rs. 200Rs.200

Rs.250Rs. 250Rs.250

Solution

Question 4

300030003000

600060006000

120001200012000

150001500015000

Solution

Question 5

No loss or gain

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

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

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

None of these

Solution

Question 6

C=10+3PC = 10 + 3PC=10+3P

C=10P+3C = 10P + 3C=10P+3

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

C=9+3PC = 9 + 3PC=9+3P

C=10P−7C = 10P - 7C=10P−7

Solution

Question 7

Rs. 630630630

Rs. 700700700

Rs. 780780780

Rs. 680680680

Solution

Question 8

Rs 3.3\text{Rs }3.3Rs 3.3

Rs 5\text{Rs }5Rs 5

Rs 7\text{Rs }7Rs 7

Rs 9\text{Rs }9Rs 9

Rs 11\text{Rs }11Rs 11

Solution

Question 9

Rs. 76.50Rs.\ 76.50Rs. 76.50

Rs. 75Rs.\ 75Rs. 75

Rs. 80Rs.\ 80Rs. 80

Rs. 77Rs.\ 77Rs. 77

Solution

Question 10

19,750

17,950

19,950

19,000

Solution

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$494.44$

$666.66$

$840$

$942$

A makes Rs. $1100$ on the deal

A makes Rs. $1000$ on the deal

A loses Rs. $900$ on the deal

$Rs. 110$

$Rs. 140$

$Rs. 200$

$Rs. 250$

$3000$

$6000$

$12000$

$15000$

Loss of $\text{Rs. } 1000$

Gain of $\text{Rs. } 1000$

Gain of $\text{Rs. } 2000$

$C = 10 + 3P$

$C = 10P + 3$

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

$C = 9 + 3P$

$C = 10P - 7$

Rs. $630$

Rs. $700$

Rs. $780$

Rs. $680$

$\text{Rs }3.3$

$\text{Rs }5$

$\text{Rs }7$

$\text{Rs }9$

$\text{Rs }11$

$Rs.\ 76.50$

$Rs.\ 75$

$Rs.\ 80$

$Rs.\ 77$