Question 1: Find the selling price when:

i) C.P. $=$ Rs. $7640$ Gain $=15\%$           ii) C.P. $=$ Rs. $4850$, Loss $=12\%$

iii) C.P. $=$ Rs. $720$, Loss $= 8\frac{3}{4} \%$          iv) C.P. $=$ Rs. $2652$, Gain $= 16\frac{2}{3} \%$

i)  C.P. $=$ Rs. $7640$ Gain $=15\%$

$S.P. = \Big( 1+$ $\frac{15}{100}$ $\Big) \times 7640=8786$ Rs.

ii)  C.P. $=$ Rs. $4850$, Loss $=12\%$

$S.P. = \Big( 1-$ $\frac{12}{100}$ $\Big) \times 4850=4268$ Rs.

iii)  C.P. $=$ Rs. $720$, Loss $= 8\frac{3}{4} \%$

$S.P. = \Big( 1-$ $\frac{8\frac{3}{4}}{100}$ $\Big) \times 720=657$ Rs.

iv)  C.P. $=$ Rs. $2652$, Gain $= 16\frac{2}{3}\%$

$S.P. = \Big( 1+$ $\frac{16\frac{2}{3}}{100}$ $\Big) \times 2652=3094$ Rs.

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Question 2: Find the Cost Price, When:

i) S.P. $=$ Rs. $207$, Gain $15\%$          ii) S.P. $=$ Rs. $448.20$, Loss $17\%$

iii) S.P. $=$ Rs. $1479$, Gain $6 \%$          iv) S.P. $=$ Rs. $611.80$, Loss $8\%$

i)  S.P. $=$ Rs. $207$, Gain $15\%$

$C.P. = \Big($ $\frac{100}{100+15}$ $\Big) \times 207=180$ Rs.

ii)  S.P. $=$ Rs. $448.20$, Loss $17\%$

$C.P. = \Big($ $\frac{100}{100-17}$ $\Big) \times 448.20=540$ Rs.

iii)  S.P. $=$ Rs. $1479$, Gain $6 \%$

$C.P. = \Big($ $\frac{100}{100+6 \frac{1}{4}}$ $\Big) \times 1479=1392$ Rs.

iv)  S.P. $=$ Rs. $611.80$, Loss $8\%$

$C.P. = \Big($ $\frac{100}{100-8}$ $\Big) \times 611.80=665$ Rs.

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Question 3: A Sells a cycle to B at a Profit of $20\%$ and B Sells it to C at a Profit of $5\%$. If C pays Rs. $3780$, What did A Pay for it?

Let C.P. of A $= x$

Then, S.P. of A $=$ C.P. of B $= 1.2 x$

S.P. of B $= (1.2x) \times (1.05) =1.26x$

Therefore

$1.26 x = 3780$

$x = 3000$

Hence A Paid Rs. $3000$ for the cycle.

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Question 4: A Sold a watch to B at $12\%$ gain and B had to sell if it Manu at a loss of $5\%$. If C Paid Rs. $5320$ then how much did A Pay?

Let C.P. of A $= x$

C.P. of B $=1.12x$

Then, S.P. of A $=$ C.P. of B $= 1.2 x$

S.P. of B $= (1.12x) \times (0.95) =1.064x$

Therefore

$1.064 x = 5320$

$x = 5000$

Hence A Paid Rs. $5000$ for the Watch

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Question 5: A Grocer Purchase $80$ kg of Rice at Rs. $27/Kg$ and mixed it with $120$ kg of rice purchased at Rs. $32/kg$. At what rate per kg should he sell the mixture to gain $16\%$?

Let Total C.P. $= 80 \times 27 + 120 \times 32 = 6000$

For $16\%$ gain Total S.P. $= \Big($ $\frac{100+16}{100}$ $\Big) \times 6000=6960$

Total Quantity $= 80 + 120 = 200 kg$

Hence S.P. per kg $=$ $\frac{6960}{200}$ $=34.8 Rs. /kg$

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Question 6: A Bought two bags for Rs. $1150$ each. A the sold one of them at a gain of $6\%$ and the other at a loss of $2\%$. How much did A Gain?

Total C.P. $= 1150 \times 2 = 2300$ Rs.

Total S.P. $= \Big($ $\frac{100+6}{100}$ $\Big) \times 1150+ \Big($ $\frac{100-2}{100}$ $\Big) \times 1150$

$= 1219 + 1127 = 2346$ Rs.

$Gain \% = \Big($ $\frac{2346-2300}{2300}$ $\Big) \times 100=2\%$

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Question 7: A trader purchased a wall clock and a watch for a sum of Rs. $5070$. He sold them making a profit of $10\%$ on the wall clock and $15\%$ on the watch he earns Rs. $699.50$. Find the cost price of the wall clock and that of the watch.

Let the C.P. of wall clock $= {x}$

Let the C.P. of wall clock $= {y}$

Therefore

$\ {x + y} = 5070$

Also $\ 1.1{x} + 1.15{y} = 5070 + 669.5 \ = 5739.5$

Solving for ${x} \ and \ {y}$ we get

${x} =1820 Rs. \ or \ {y} = 3250$ Rs.

Hence Cost of Wall Clock $=1820 Rs.$ and Cost of Watch $= 3250$ Rs.

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Question 8: Toffees are bought at $15$ for Rs. $20$. How many toffees would be sold for Rs. $20$ so as to gain $25\%$?

C.P. of 15 Toffees $= Rs. 20$

Therefore, C.P. of 1 Toffee $=$ $\frac{20}{15}$ Rs.

For $25\%$ gain, S.P. of 1 Toffee $=$ $\frac{20}{15}$ $\times 1.25 =$ $\frac{25}{15}$ Rs.

Therefore number of toffees that you can sell in $20$ Rs $=$ $\frac{20}{25/15}$ $=$ $\frac{20 \times 15}{25}$ $=12$ Toffees

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Question 9: Two-thirds of a consignment was sold at a profit of $5\%$ and the remaining at a loss of $2\%$. If the total profit was Rs. $4000$, Find the value at which the consignment was purchase?

Let the C.P. of Consignment $= \textit{x}$

Therefore

$\frac{2}{3}$ $x \times 1.05+$ $\frac{1}{3}$ $x \times 0.98=x+4000$

$\frac{70}{100}$ $x+$ $\frac{98}{300}$ $x=x+4000$

$\frac{8}{300}$ $x=4000 \ or \ x=150000 Rs$

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Question 10: A Grocer bought sugar worth Rs. $4500$. He sold $1/3$ of it at $10\%$ Gain. At what gain $\%$ the remaining sugar be sold to have a $12\%$ gain on the whole?

C.P. of sugar $= 4500$ Rs.

Let the $Gain \%$ of on the remaining sugar $= \textit{x }\%$

Therefore

$\frac{1}{3}$ $\times 4500 \times 1.1+$ $\frac{2}{3}$ $\times 4500 \times \ \Big( 1+$ $\frac{x}{100}$ $\Big) =4500 \times 1.12$

$1650+3000+30x=5040 \ or \ x=13\%$

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Question 11: A Man buys a piece of land for Rs. $38400$. He sells $2/5$ of at a loss of $6\%$. At what Gain $\%$, the remaining piece of land be sold to gain $10\%$ on the whole?

C.P. of land $= 38400$ Rs.

$\frac{2}{5}$ the of land sold at a loss of $6\%$

Let’s the remainder be sold at $x \%$ gain

Therefore

$\frac{2}{5}$ $\times 38400 \times 0.94+$ $\frac{3}{5}$ $\times 38400\ \times \Big( 1+$ $\frac{x}{100}$ $\Big) =38400 \times 1.1$

$14438.4+23040(1+0.01x)=42240$

Solving for $x$ we get $x =20$ $\frac{2}{3}$ $\%$

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Question 12: By Selling a car for Rs. $10416$, a man gain $12\%$. What will be his gain or loss percent if it is sold for Rs. $9114$.

Let the cost of the car $= x$

Therefore,

$\Big( 1+$ $\frac{12}{100}$ $\Big) x=10416 \ or \ x=9300$ Rs.

$x = 9300$ Rs.

If S.P $= Rs. 9114$

$Loss \%= \Big($ $\frac{9300-9114}{9300}$ $\Big) \times 100=2\%$

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Question 13: A Chair sold for Rs. $2142$ at a Gain at $5\%$ At what price should it be sold to gain $10\%$

Let The C.P. of chair $= {x}$

Then, $\Big( 1+$ $\frac{5}{100}$ $\Big) x=2142 or x=2040$ Rs.

For $10\%$ Gain

S.P. $= \Big( 1+$ $\frac{10}{100}$ $\Big) \times 2040=2244$ Rs.

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Question 14: A television is sold for Rs. $9360$ at a loss of $4\%$. For how much it should have been sold be gain $4\%$?

Let the C.P. of Television $= {x}$

$\Big( 1-$ $\frac{4}{100}$ $\Big) x=9360 or x=9750 Rs$

To gain $4\%,$

S.P. $= \Big( 1+$ $\frac{4}{100}$ $\Big) \times 9750=10140$ Rs.

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Question 15: A shop keeper sold two fans at Rs. $1980$ each. On one he gained $10\%$, while other he cost $10\%$. Calculate the gain or loan percent on whole transaction?

Let C.P. of $1^{st}$ fan $= {x}$ Rs.

Let C.P. of $2^{nd}$ fan $= {y}$ Rs.

Therefore, $\Big( 1+$ $\frac{10}{100}$ $\Big) x=1980 or x=1800$

Similarly $\Big( 1-$ $\frac{10}{100}$ $\Big) y=1980 or y=2200$

Hence, Total C.P. $= 1800 + 2200 = 4000$ Rs.

Total S.P. $= 2 \times 1980 = 3960$ Rs.

$Loss \%= \Big($ $\frac{4000-3960}{4000}$ $\Big) \times 100=1\%$

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Question 16: Shanti sold two cameras for Rs. $6555$ each. On one she lost $5\%$, while on the other she gained $15\%$. Find the gain or loss percentage in whole transaction.

Let, C.P. of $1^{st}$ Camera $= {x}$

Let C.P. of $2^{nd}$ Camera $= {y}$

Therefore, $\Big( 1-$ $\frac{5}{100}$ $\Big) x=6555 or x=6900$

Similarly $\Big( 1+$ $\frac{15}{100}$ $\Big) y=6555 or y=5700$

Total C.P. $= 6900 + 5700 = 12600$ Rs.

Total S.P. $= 2 \times 6555 = 13110$ Rs.

$Gain \%= \Big($ $\frac{13110-12600}{12600}$ $\Big) \times 100=4$ $\frac{1}{21}$ $\%$

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Question 17: By selling $45$ lemons for Rs. $40$, a man loses $20\%$ how many should he sell for Rs. $24$ to gain $20\%$ on the transaction.

Let C.P. of a lemon $= x$ Rs.

S.P. of one Lemon $=$ $\frac{40}{45}$  Rs.

Therefore $\Big( 1-$ $\frac{20}{100}$ $\Big) x=$ $\frac{40}{50}$ $\ or \ x=$ $\frac{10}{9}$  Rs.

To gain $20\%$ on the transaction,

S.P. of one Lemon $= \Big( 1+$ $\frac{20}{100}$ $\Big) \times$ $\frac{10}{9}$ $=\$ $\frac{4}{3}$ Rs

Need to be sold for $24$ Rs. $=$ $\frac{24}{4/3}$ $=18$ Lemons

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Question 18: A sold a pressure cooker at a loss of $8\%$. Had she bought it at $10\%$ less and sold for Rs. $176$ more, she would have gained $20\%$. Find the cost price of the pressure cooker.

Let the cost of pressure cooker $= x$

S.P. $= 0.92x$

New C.P. $= 0.9x$

New S.P. $= 0.92x + 176$

Therefore $Gain \%$

$\frac{0.92x+176-0.9x}{0.9x}$ $=$ $\frac{20}{100}$

$\frac{0.2x+176}{0.9x}$ $=$ $\frac{20}{100}$

$2x+17600=8x \ or \ x=1100$ Rs.

Cost of the cooker $= 1100$ Rs.

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Question 19: A Man sold a toaster at a profit of $10\%$. Had he purchased of for $5\%$ less and sold it for $56$ Rs. more, he would have gained $25\%$. How much did he buy for?

Let, C.P. of Toaster $= x$

S.P. of Toaster $= 1.1x$

New C.P. $= 0.95x$

New S.P. $=1.1x + 56$

Gain $= 25\%$

Therefore: $\frac{1.1x+56-0.95x}{0.95x}$ $=$ $\frac{25}{100}$

$\frac{0.15x+56}{0.95x}$ $=$ $\frac{25}{100}$

$15x+5600=23.75x \ or \ x=640$ Rs.

The man bought the toaster for Rs. 640

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Question 20: A shopkeeper sells each of his goods at a gain of . If on any day, his total sell was Rs. $9408$, what was?

i) The total cost of all goods sold on that day          ii) His profit of that day

Let the total C.P. of goods $= x$
$\Big( 1+$ $\frac{22.5}{100}$ $\Big) x=9408 or x=7680$ Rs.
Profit for day $= 9408-7680 =1728$ Rs.