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MATHS 5 Marks Questions

Profit and Loss · UP Board (UPMSP) STD 8 (UPMSP - English Medium). 8 questions.

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8 questions · timed · auto-graded

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 $200\ kg$ of rice at $Rs.25/kg$. He sold $80\ kg$ of it at a gain of $10\%$ and $40\ kg$ at a loss of $4\ %.$ At what rate/kg should he sell the remainder to gain $8\%$ on his total investment$?$
Answer
$CP$ of $1\ \ kg$ of rice $= Rs. 25$
$C.P$ of $200\ \ kg$ rice $= Rs. (200 \times 25) = Rs. 5000 $
$Rs. (200 \times 25) = Rs. 5000 $
$CP$ of $80\ \ kg$ of rice $= Rs. (25 \times 80) = Rs. 2000 $
$CP$ of $40\ kg$ of rice $= Rs (25 \times 40) = Rs. 1000 $
$Rs. (25 \times 40) = Rs. 1000$
$SP$ of $80\ kg$ of rice $=\frac{100+\text{gain}\%}{100}\times\text{CP}$
$=\text{Rs.}\frac{110}{100}\times2000$
$ =\text{Rs. }2200$
$SP$ of $40\ kg$ rice
$=\frac{100+\text{loss}\%}{100}\times\text{CP}$
$=\text{Rs. }\frac{96}{100}\times1000$
$= \text{Rs. }960$ SP of 200\ kg rice
$=\frac{100+\text{gain}\%}{100}\times\text{CP}$
$=\text{Rs.}\frac{108}{100}\times5000$
$= \text{Rs. }5400$
Remaining quantity of rice $= (200 - 80 + 40)\ kg = 80\ kg$
​SP of the remaining rice $(80\  \ kg) = Rs. (5400 - 2200 - 960) = Rs. 224$
$\therefore \text{Rate}/\text{kg}=\text{Rs. }\frac{2240}{80}=\text{Rs. }28$
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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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