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MATHS 2 Marks Questions

Comparing Quantities · UP Board (UPMSP) STD 8 (UPMSP - English Medium). 13 questions.

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2 Marks Questions

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13 questions · timed · auto-graded

Question 12 Marks
A watch worth Rs. $5400$ is offered for sale at Rs. $4,500$. What per cent discount is offered during the sale?
Answer
Marked price of a watch = Rs. $5400$
Selling price = Rs. $4500$
Discount = Marked price – Selling price = Rs. $5400$ – Rs. $4500$
= Rs. $900$ $\text{Discount}\%=\frac{\text{Discount}}{\text{Marked price}}\times100$
$=\frac{900}{5400}\times100$
$=\frac{900}{54}=\frac{450}{27}=\frac{150}{9}=\frac{50}{3}\%$
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Question 22 Marks
Rain forests are home to $90,000$ of the $2,50,000$ identified plant species in the world. What per cent of the world’s identified plant species are found in rain forests?
Answer
$90000$ of the $250000$ identified plant species in the world are specified as rain forest
In percentage$=\frac{90000}{2500000}\times100=\frac{900}{25}=36\%$
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Question 32 Marks
Store $A$ and Store $B$ both charge Rs. $750$ for a video game. This week the video game is on sale for Rs. $600$ at Store $B$ and for $25%$ off at Store $A$. At which store is the game less expensive?.
Answer
Video game available in store $A$ & store $B$ at rate = Rs. $750$
Store $B$ sells video game on sale offer = Rs. $600$
Store $A$ sells video game at discount $= 25\%$
So, the price of video game at store $B$$=750-\frac{25}{100}\times750=750-187.5=\text{Rs.} \ 562.5$
Hence, at sore $A$ the video game is less expensive.
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Question 42 Marks
Prachi bought medicines from a medical store as prescribed by her doctor for Rs. $36.40$ including $4\%$ $VAT$. Find the price before $VAT$ was added.
Answer
The cost of medicine including $4\%$ $VAT$ $= Rs.$ $36.40$
The price of medicine before $4\%$ $VAT$$=36.40-\frac{4}{100}\times36.40$
$=36.40-4\times0.364$
$=36.40-1.456=$$\text{Rs.} \ 34.944=\text{Rs}. \ 35$
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Question 52 Marks
On selling a chair for $Rs. 736$, a shopkeeper suffers a loss of $8\%$. At what price should he sell it so as to gain $8\%$?
Answer
Let the cost price of a chair $= Rs.\ x$
Selling price of a chair $= Rs.\ 736$
At selling a shopkeeper suffers $8\%$ loss.
According to the question,$\text{x}-\text{x}\times\frac{8}{100}=736$
$\frac{92\text{x}}{100}=736$
$\text{x}=\frac{73600}{92}=\text{Rs.}800$
To gain $8\%$ profit the price should be$=800+\frac{8}{100}\times800$
$=800+64=\text{Rs.} \ 864$
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Question 62 Marks
In a factory, women are $35\%$ of all the workers, the rest of the workers being men. The number of men exceeds that of women by $252$. Find the total number of workers in the factory.
Answer
Percentage of women in factory $= 35\%$
Percentage of men in factory $= 100 - 35 = 65\%$
Let the number of persons in the factory be $x$.
According to the question,$\text{x}\times\frac{65}{100}-\text{x}\times\frac{35}{100}=252$
$\frac{65\text{x-}\text{35x}}{100}=252$
$\frac{30\text{x}}{100}=252$
$\text{x}=\frac{2520}{3}=840$
Hence, total number of workers in the factory is $840$.
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Question 72 Marks
A dining table is purchased for $Rs.\ 3,200$ and sold at a gain of $6\%$. If a customer pays sales tax at the rate of $5\%$. How much does the customer pay in all for the table?
Answer
The cost price of the dinning table $= Rs.\ 3200$
The dinning table sold at a gain of $6\%$
So, selling price of the dinning table$=3200+\frac{6}{100}\times3200=3200+192=\text{Rs.} \ 3392$
Also, customer pay sale tax $=5\%$
Selling price with sales tax$=3392+3392\times\frac{5}{100}=3392+169.6=\text{Rs.} \ 3561.60$
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Question 82 Marks
At a toy shop price of all the toys is reduced to $66\%$ of the originalprice.
$a.$ What is the sale price of a toy that originally costs $Rs.\ 90$?
$b.$ How much money would you save on a toy costing $Rs.\ 90$?
Answer
$a.$ Original cost of the toy $= Rs.\ 90$ If price, reduce to $66\%$ of the original price, then price became
$=90-\frac{66}{100}\times90=90-59.4=\text{Rs.} \ 30.6$
$b.$ We have discounted amount$=66\%\ \ \text{of} \ 90=\frac{66}{100}\times90=\text{Rs.} \ 59.4$
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Question 92 Marks
The human body is made up mostly of water. In fact, about $67\%$ of a person’s total body weight is water. If Jyoti weights $56\ kg$, how much of her weight is water?
Answer
Jyoti’s weight $= 56\ kg$ Where $67\%$ of a person is total body weight is water.
Water in Jyoti body$=\frac{67}{100}\times56=\frac{3752}{100}=37.52\text{kg}$
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Question 102 Marks
The per cent of pure gold in $14$ carat gold is about $58.3\%$. A $14$ caratgold ring weighs $7.6$ grams. How many grams of pure gold are in the ring?
Answer
The percentage of gold in $14$ carat gold $= 58.3\%$
Weight of $14$ carat gold $= 7.6\ g$
Pure gold in $14$ carat gold of $7.6\text{g}=7.6\times\frac{58.3}{100}=\frac{443.08}{100}=4.431\text{g}$
Hence, pure gold in $7.6\ g$ of $14$ carat gold is equal to $4.431\ g$.
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Question 112 Marks
Music $CD$ originally priced at $Rs.\ 120$ is on sale for $25\%$ off. What is the $S.P.$? Sonia and Rahul have different ways of calculating the sale price for the items they bought.

As you work on the next problem, try both of these methods to see which you prefer.
Answer
Original price of music $CD = Rs.120$
$25\%$ discount on $Rs.\ 120$,
if sale is applicable$=120\times\frac{25}{100}=\frac{120}{4}=\text{Rs.} \ 30$
$\text{Discount}=\text{Rs.} \ 30$
Selling price after discount $=\text{Rs.} \ 120-\text{Rs.} \ 30=\text{Rs.} \ 90$
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Question 122 Marks
Kritika ordered one pizza and one garlic bread from a pizza store and paid $Rs.\ 387$ inclusive of taxes of $Rs.\ 43$. Find the tax$\%$.
Answer
The cost of $1$ pizza & $1$ garlic bread inclusive as tax $= Rs.\ 43$
The cost of $1$ pizza & $1$ garlic bread without tax $= Rs.\ 387 − Rs.\ 43 = Rs.\ 344$
$\text{Tax}\%=\frac{43}{100}\times100=\frac{100}{8}=12.5\%$
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Question 132 Marks
During school hours, Neha finished $73 \%$ of her homework and Minakshi completed $5/8$ of her homework. Who must finish a greater per cent of homework?
Answer
Neha finished her homework in percentage$=73\%=\frac{73}{100}$
Where Minakshi completed =$\frac{5}{8}$of her homework Home work left for Minakshi completed $=1-\frac{5}{8}=\frac{3}{8}$
In percentage $=\frac{3}{8}\times100=37.5\%$
Homework left for Neha$=(100-73)=27\%=\frac{27}{100}$
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