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Maths 1 Marks Question

Direct and Inverse Proportion · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 21 questions.

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Question 11 Mark
From the following table, determine if $x$ and $y$ are in direct proportion or not.
$X$ $1$ $4$ $9$ $20$
$Y$ $1.5$ $6$ $13.5$ $30$
Answer
In direct proportion,$\frac{\text{x}}{\text{y}}=\text{k}$(constant) For table $(c),$
$X$ $1$ $4$ $9$ $20$
$Y$ $1.5$ $6$ $13.5$ $30$
$\frac{1}{1.5},\frac{1}{1.5},\frac{1}{1.5},\frac{1}{1.5}$ so, $(c)$ is in direct proportion.
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Question 21 Mark
Income tax and the income.
Answer
Income tax and the income are directly proportional to each other, e.g. Let Mr $X$ have $4.5$ lakh annual income. Then, he pay $10\%$ income tax on his income. But if Mr $X$ have $5.5$ lakh annual income, then he has to pay $30\%$ incometax on his salary/income.
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Question 31 Mark
It is given that l varies directly as $m?$ Find the constant of proportion $(k),$ when l is $6$ then $m$ is $18.$
Answer
If $l = 6$ and $m = 18,$ then $\text{k}=\frac{6}{18}=\frac{1}{3}$
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Question 41 Mark
The number of people working and the time to complete a given work
Answer
The number of people working and the time to complete a given work are inversely proportional to each other. e.g. Let $20$ workers can complete a work in $1$ day. Then, $10$ workers can complete the same work in $2$ days.
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Question 51 Mark
Area of the walls of a room and the cost of white washing the walls.
Answer
Area of the walls of a room & the cost of white washing the walls are directly proportional to each other. e.g., Let $Rs.1000$ required for white washing a room with $(12 × 8)m$ size. Then, $Rs. 2000$ required for white washing a room with $(12 × 16)m$ size.
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Question 61 Mark
If $25$ metres of cloth costs $Rs 337.50,$ then
What will be the cost of $40$ metres of the same type of cloth$?$
Answer
$25m$ of cloth cost $= Rs. 337.50$
$1m$ of cloth cost$=\text{Rs.}\frac{337.50}{25}$
Cost of 40m of the same type of cloth $=\frac{337.50}{25}\times40=\frac{13500}{25}=\text{Rs.}540$
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Question 71 Mark
The distance travelled by $CNG$ bus and the amount of $CNG$ used.
Answer
The distance travelled by $CNG$ bus and the amount of $CNG$ used are directly proportional. e.g., Let a $CNG$ bus can travelled $10\ km$ in $1\ kg$ of $CNG.$ Then, the same $CNG$ bus travelled $20\ km$ in $2 × 1 = 2\ kg$ of $CNG.$
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Question 81 Mark
Increase in cost and number of shirts that can be purchased if the budget remains the same.
Answer
Increase in cost and number of shirts that can be purchased, if the budget remains the same are inversely proportional to each other, e.g. Let $2$ shirts price $= Rs.800$ After increasing in price of each shirt, $1$ shirt price became $Rs.800$ where budget $=Rs.800$
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Question 91 Mark
Sales Tax and the amount of the bill.
Answer
Sales tax & the amount of the bill are directly proportional to each other. e.g.,
Let bill amount $= Rs.1000$
sales tax $= 10\%$
Then, sales tax$=\frac{10}{100}\times10000 \text{ Rs.}100$
But, bill amount $= 2000$
Sales tax $= 10\%$
Then, sales tax$=\frac{10}{100}\times2000=10\times20=\text{Rs.}2000$
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Question 101 Mark
The quantity of rice and its cost.
Answer
The quantity of rice and its cost are directly proportional to each other, e.g. Let $1\ kg$ of rice price $= Rs.40$ Then, $2\ kg$ of rice price $= Rs.2 × 40 = Rs.80$
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Question 111 Mark
If $25$ metres of cloth costs $Rs. 337.50,$ then What will be the length of the cloth bought for $Rs.810?$
Answer
$25m$ of cloth cost $= Rs. 337.50$
$1m$ of cloth cost$=\text{Rs.}\frac{337.50}{25}$
The length of cloth bought for $Rs. 810 =\frac{810\times25}{337.50}=\frac{20250}{337.50}=60\text{cm}$
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Question 121 Mark
It is given that l varies directly as $m.$ Find $m$ when l is $8.$
Answer
If ${\text{l}}={8}$
$\frac{\text{l}}{\text{m}}=\text{k}$
$\frac{8}{\text{m}}=\frac{1}{3}$
$\text{m}=8\times3=24$
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Question 131 Mark
The number of people working and the quantity of work.
Answer
The number of people working & the quantity of work are directly proportional to each other. e.g., Let $20$ workers can complete $20\% $ work. Then, $40$ workers can complete 40% of the same work.
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Question 141 Mark
Compound interest on a given sum and the sum invested.
Answer
Compound interest on a given sum & the sum invested are neither depend directly nor inversely.
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Question 151 Mark
Area of land and its cost.
Answer
Area of land & cost are directly proportional to each other. e.g. Let $200m^2$ land cost $= Rs. 5000$ then, $400m^2$ land cost $= Rs.10000$
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Question 161 Mark
Distance travelled by an auto-rickshaw and time taken.
Answer
Distance travelled by an auto rickshaw and time taken are directly proportional to each other. e.g., Let an auto rickshaw takes $2h$ to travel $10\ km .$ Then, it will take $4h$ to travel $20k.$
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Question 171 Mark
It is given that l varies directly as $m?$ Find l, when $m$ is $33.$
Answer
If $m = 33,$ then $\frac{\text{l}}{\text{m}}=\frac{1}{3}$ $\frac{\text{l}}{33}=\frac{1}{3}$$\text{l}=\frac{33}{8}=11$
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Question 181 Mark
The time taken by a train to cover a fixed distance and the speed of the train.
Answer
The time taken by a train to cover a fixed distance and the speed of the train are inversely proportional. e.g., Let a train cover $100\ km$ in $1\ h$ with speed $100\ km/ h.$ Then, the same train cover $100\ km$ in $30\ min$ with speed $200\ km/ h$
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Question 191 Mark
Simple interest on a given sum and the rate of interest.
Answer
Simple interest on a given sum & the rate of interest are directly proportional to each other. e.g., Let $P = Rs.1000, R = 10\%, T = 1\ yr.$
$\text{SI}=\frac {\text {P} \times R \times T}{100}=\frac{1000\times20\times1}{100}=\text{Rs.200}$
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Question 201 Mark
Number of students in a hostel and consumption of food.
Answer
No. of students in a hostel & consumption of food are directly proportional to each other. E.g., Let $200$ students in a hostel can consume $100\ kg$ of rice in a month. Then, $400$ students in a hostel consume $200\ kg$ rice in a month.
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Question 211 Mark
It is given that $l$ varies directly as $m?$ Write an equation which relates $l$ and $m.$
Answer
Equation related to $l$ and $m$ is $\frac{\text{l}}{\text{m}}=\text{k}$ (constant)
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