5 Mark Question

Question 15 Marks

Ahmed buys a plot of land for Rs. 480000. He sells of it at a loss of 6%. At what gain percent should he sell the remaining part of the plot to gain 10% on the whole?

Answer

CP of the plot of land = Rs. 4,80,000
CP of $\frac{2}{5}\text{th}$ of the land $=\frac{2}{5}\times480000=\text{Rs. }1,92,000$
Loss on $\frac{2}{5}\text{th}$ of the land = 6%
SP of $\frac{2}{5}\text{th}$ of the land = CP - Loss
$=192000-\frac{6}{100}\times19200=\text{Rs. }1,80,480$
CP of $\frac{3}{5}\text{th}$ of the land = 480000 - 192000 = Rs. 2,88,000
Total gain % = 10%
Total gain $=\frac{10}{100}\times480000=\text{Rs. }48,000$
Total SP = CP + Gain = Rs. 4,80,000 + Rs. 48,000 = Rs. 5,28,000
SP of $\frac{3}{5}\text{th}$ of the land = Rs. 5,28,000 - Rs. 1,80,480 = Rs. 3,47,520
Gain on $\frac{3}{5}\text{th}$ of the land = SP of $\frac{3}{5}\text{th}$ land - CP of $\frac{3}{5}\text{th}$ land
= Rs. 3,47,520 - Rs. 2,88,000 = Rs. 59,520
Gain % on seling the remaining part of the plot
$=\frac{\text{gain}}{\text{CO of }\frac{3}{5}\text{th land}}\times100\%=\frac{59520}{288000}\times100\%=20\frac{2}{3}\%$

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Question 25 Marks

Vinod sold a watch to Arun at a gain of 12% and Arun had to sell it to Manoj at a loss of 5%. If manoj paid Rs. 3990 for it, how much did vinod pay for the watch?

Answer

Let the CP of the watch for Vinod be Rs. x.
SP = Gain + CP
$=12\%\text{ of CP}+\text{x}$
$=\frac{12}{100}\text{x}+\text{x}$
$=\text{Rs. }\frac{112}{100}\text{x}$
Now,
SP of the water for Vinod will be the CP of the watch for Arun.
SP of the watch for Arun
= CP - Loss
$=\frac{112}{100}\text{x}-5\%\text{ of }\frac{112}{100}\text{x}$
$=\frac{112}{100}\text{x}-\frac{5}{100}\Big(\frac{112}{100}\text{x}\Big)$
$=\frac{112}{100}\text{x}\Big(1-\frac{5}{100}\Big)$
$=\text{Rs. }\frac{112}{100}\text{x}\Big(\frac{95}{100}\Big)$
SP of the watch for Arun will be the CP of the watch for Manoj.
But, CP of the watch for Manoj = Rs. 3,990
So,
$\frac{112}{100}\text{x}\Big(\frac{39}{100}\Big)=3990$
$\Rightarrow\text{x}=\frac{3990\times100\times100}{112\times95}=3750$
Thus, Vinod paid Rs. 3,750 for the watch.

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Question 35 Marks

A dealer sold a camera for Rs. 1080 gaining $\frac{1}{8}$ of its cost price. Find (i) the cost price of the camera, and (ii) the gain percent earned by the dealer.

Answer

SP of the camera = Rs. 1080
Let Rs x be the CP
Gain $=\text{Rs. }\frac{1}{8}\text{x}\dots(\text{i})$
Also, gain = SP - CP
= Rs. (1080 - x) ...(ii)
From (i) and (ii), we have:
$\frac{1}{8}\text{x}=1080-\text{x}$
⇒ x = 8640 - 8x
⇒ 9x = 8640
⇒ x = 960
$\therefore$ CP = Rs. 960
Now, gain $=\frac{1}{8}\text{x}=\frac{960}{8}=\text{Rs. }120$
$\therefore$ Gain percentage $=\Big(\frac{120}{960}\times100\Big)\%=12\frac{1}{2}\%$

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Question 45 Marks

Luxmi sold two sarees for Rs. 1980 each. On one, she lost 10%, while on the other she gained 10%. Find her gain or loss percent in the whole transaction.

Answer

SP of first saree = Rs. 1,980
Loss = 10%
Let the CP of first saree be Rs. x
CP = Loss + SP
$\Rightarrow\frac{10}{100}\times\text{x}+1980=\text{x}$
$\Rightarrow\text{x}-\frac{10}{100}\text{x}=1980$
$\Rightarrow\frac{90}{100}\text{x}=1980$
$\Rightarrow\text{x}=2200$
$\therefore$ CP of first saree = Rs. 2,200
SP of second saree = Rs. 1,980
Gain = 10%
Let the CP of second saree be Rs. y
CP = SP - Gain
$\Rightarrow1980-\frac{10}{100}\times\text{y}=\text{y}$
$\Rightarrow1980-\frac{\text{y}}{10}\times\text{y}=\text{y}$
$\Rightarrow\text{y}+\frac{\text{y}}{10}=1980$
$\Rightarrow\frac{\text{11y}}{10}=1980$
$\Rightarrow\text{y}=1800$
$\therefore$ CP of second saree = Rs. 1,800
Total CP of two sarees = CP of first saree + CP of second saree
= Rs. 2,200 + Rs. 1,800 = Rs. 4,000
Total SP of two sarees = SP of first saree + SP of second saree
= Rs. 1,980 + Rs. 1,980 = Rs. 3,960
Here, Total CP of two sarees > Total SP of two sarees
Loss = Total CP of two sarees - Total SP of two sarees
= Rs. 4,000 - Rs. 3,960 = Rs. 40
$\therefore$ Loss% in the whole transaction
$=\frac{\text{loss}}{\text{total CP of two sarees}}\times100\%=\frac{40}{4000}\times100\%=1\%$

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Question 55 Marks

Meenakshi sells a pen for Rs. 54 and loses $\frac{1}{10}$ of her outlay. Find (i) the cost price of the pen, and (ii) the loss percent.

Answer

SP of the pen = Rs. 54
Let Rs. x be the CP of the pen
Loss $=\text{Rs. }\frac{\text{x}}{10}$
SP - CP - loss
$=\text{x }-\frac{\text{x}}{10}$
$=\text{Rs. }\frac{\text{9x}}{10}$
Now, we have $\frac{\text{9x}}{10}=54$
$\Rightarrow\text{x}=54\times\frac{10}{9}$
$\Rightarrow\text{x}=60$
$\therefore$ CP pf the pen = Rs. 60
Now, loss $=\frac{\text{x}}{10}=\frac{60}{10}=\text{Rs. }6$
$\therefore$ Loss percentage $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{6}{60}\times100\Big)\%=10\%$

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Question 65 Marks

A grocer purchased 200kg of rice at Rs 25/kg. He sold 80kg of it at a gain of 10% and 40kg at a loss of 4%. At what rate/kg should he sell the remainder to gain 8% on his total investment?

Answer

CP of 1kg of rice = Rs. 25
C.P of 200kg rice = Rs. (200 × 25)
= Rs. 5000 Rs. (200 × 25) = Rs. 5000
CP of 80kg of rice = Rs. (25 × 80) = Rs. 2000
CP of 40kg of rice = Rs (25 × 40)
= Rs. 1000 Rs. (25 × 40) = Rs. 1000
SP of 80kg of rice $=\frac{100+\text{gain}\%}{100}\times\text{CP}$
$=\text{Rs.}\frac{110}{100}\times2000$
$ =\text{Rs. }2200$
SP of 40kg rice $=\frac{100+\text{loss}\%}{100}\times\text{CP}$
$=\text{Rs. }\frac{96}{100}\times1000$
$= \text{Rs. }960$
SP of 200kg rice $=\frac{100+\text{gain}\%}{100}\times\text{CP}$
$=\text{Rs.}\frac{108}{100}\times5000$
$= \text{Rs. }5400$
Remaining quantity of rice = (200 - 80 + 40)kg = 80kg
SP of the remaining rice (80kg) = Rs. (5400 - 2200 - 960) = Rs. 224
$\therefore \text{Rate}/\text{kg}=\text{Rs. }\frac{2240}{80}=\text{Rs. }28$

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Question 75 Marks

A shopkeeper sold two fans for Rs. 1140 each. On one he gains 14%, while on the other he loses 5%. Calculate his gain or loss percent in the whole transaction.

Answer

SP of first fan = Rs. 1,140
Gain = 14%
Let the CP of first fan be Rs. x
CP = SP - Gain
$\Rightarrow\text{x}=1140-\frac{14}{100}\text{x}$
$\Rightarrow\text{x}+\frac{14}{100}\text{x}=1140$
$\Rightarrow\frac{114}{100}\text{x}=1140$
$\Rightarrow\text{x}=1000$
$\therefore$ CP of first fan = Rs. 1,000
SP of second fan = Rs. 1,140
Loss = 5%
Let the CP of second fan be Rs. y
CP = Loss + SP
$\Rightarrow\text{y}=\frac{5}{100}\text{y}+1140$
$\Rightarrow\text{y}-\frac{5}{100}\text{y}=1140$
$\Rightarrow\frac{95}{10}\text{y}=1140$
$\Rightarrow\text{y}=1200$
$\therefore$ CP of second fan = Rs. 1,200
Total CP of two fans = CP of first fan + CP of second fan
= Rs. 1,000 + Rs. 1,200 = Rs. 2,200
Total SP of two fans = SP of first fan + SP of second fan
= Rs. 1,140 + Rs. 1,140 = Rs. 2,280
Here, Total SP of two fans > Total CP of two fans
Gain = Total SP of two fans - Total CP of two fans = Rs. 2,280 - Rs. 2,200 = Rs. 8
$\therefore$ Gain% on whole transaction
$=\frac{\text{gain}}{\text{total CP of two sarees}}\times100\%=\frac{80}{2200}\times100\%=3.64\%$

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Question 85 Marks

A grocer bought sugar worth Rs. 4500. He sold one-third of it at a gain of 10%. At what gain percent must the remaining sugar be sold to have a gain of 12% on the whole?

Answer

CP of sugar = Rs. 4500
Profit on one-third of the sugar = 10%
CP of one-third of the sugar $=\text{Rs. }\frac{4500}{3}=\text{Rs. }1500$
SP of one-third of the sugar $=\frac{100+\text{gain}\%}{100}\times\text{CP}$
$=\text{Rs. }\frac{110}{100}\times1500=\text{Rs. }1650$
Now, profit = Rs. (1650 - 1500) = Rs. 150
At a profit of 12%, we have
$\text{SP} \text{ of }\text{Sugar}=\frac{100+\text{gain}\%}{100}\times\text{CP}$
$=\text{Rs. }\frac{112}{100}\times4500=\text{Rs. }5040$
$\therefore$ Gain = Rs. (5040 - 4500) = Rs. 5400
Profit on the remaining amount of sugar = Rs. (540 - 150) = Rs. 390
CP of the remaining sugar = Rs. (4500 - 1500) = Rs. 3000
Gain percentage $=\Big(\frac{\text{gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{390}{3000}\times100\Big)\%=13\%$
Therefore, the profit on the remaining amount of sugar is 13%.

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