3 Mark Question

Question 13 Marks

The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people ?

Answer

Let the stock of grain last for $x$ days for 6000 people.
The number of people and the days for which stock will last are in inverse proportion.
$
\begin{aligned}
& \therefore 6000 \times x =4000 \times 30 \\
& \therefore x=\frac{4000 \times 30}{6000}=20
\end{aligned}
$
$\therefore$ The stock of grain will last for 20 days for 6000 people.

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Question 23 Marks

Mary cycles at 6 km per hour. How long will she take to reach her Aunt’s house which is 12 km away? If she cycles at a speed of 4 km/hr, how long would she take ?

Answer

Speed of the cycle $=6 km / hr$
Distance travelled to reach her Aunt's house $=12 km$
$\therefore$ Time required $=\frac{\text { Distance travelled }}{\text { Speed }}$
$=\frac{12}{6}$
$=2$ hours
Let the time required when the speed of the cycle is $4 km / hr$ be $x$ hours.

The speed of the cycle and the time required to travel the same distance are in inverse proportion.
$
\begin{aligned}
& \therefore 4 \times x =6 \times 2 \\
& \therefore x=\frac{6 \times 2}{4}=3 \text { hours }
\end{aligned}
$
$\therefore$ Mary will require 2 hours if she is cycling at $6 km / hr$ and 3 hours if she is cycling at $4 km / hr$ to reach her Aunt's house.

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Question 33 Marks

Mohanrao took 10 days to finish a book, reading 40 pages every day. How many pages must he read in a day to finish it in 8 days ?

Answer

Let Mohanrao read $x$ pages every day to finish the book in 8 days. The number of pages read per day and the days required to finish the book are in inverse proportion.
$
\begin{aligned}
& \therefore 8 \times x =10 \times 40 \\
& \therefore x=\frac{10 \times 40}{8} \\
& =50
\end{aligned}
$
$\therefore$ Mohanrao will have to read 50 pages every day to finish the book in 8 days.

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Question 43 Marks

Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take ?

Answer

Let 6 workers take $x$ days and 15 workers take $y$ days to weed the field.

The number of workers and the time required to weed the field are in inverse proportion.
$
\begin{aligned}
& \therefore 6 \times x =5 \times 12 \\
& \therefore x=\frac{5 \times 12}{6} \\
& \therefore x =10 \text { days }
\end{aligned}
$
Also, $15 \times y=5 \times 12$
$
\begin{aligned}
& \therefore y=\frac{5 \times 12}{15} \\
& =4 \text { days }
\end{aligned}
$
$\therefore 6$ workers will take 10 days and 15 workers will take 4 days to weed the field.

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Question 53 Marks

Two mobiles cost Rs 16,000. How much money will be required to buy 13 such mobiles ?

Answer

Let the cost of 13 mobiles be Rs $x$.
The quantity of mobiles and their cost are in direct proportion.
$
\begin{aligned}
& \therefore \frac{2}{16000}=\frac{13}{x} \\
& \therefore 2 x =13 \times 16000 \ldots . \text { (Multiplying both sides by } 16000 x ) \\
& \therefore x=\frac{13 \times 16000}{2}=104000
\end{aligned}
$
$\therefore$ Rs 104000 will be required to buy 13 mobiles.

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Question 63 Marks

The cost of 12 quintals of soyabean is Rs 36,000. How much will 8 quintals cost ?

Answer

Let the cost of 8 quintals of soyabean be Rs $x$.
The quantity of soyabeans and their cost are in direct proportion.
$
\begin{aligned}
& \therefore \frac{12}{36000}=\frac{8}{x} \\
& \therefore 12 x=8 \times 36000 \ldots \text { (Multiplying both sides by } 36000 x ) \\
& \therefore x=\frac{8 \times 36000}{12}=24000
\end{aligned}
$
$\therefore$ The cost of 8 quintals of soyabean is Rs 24000 .

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Question 73 Marks

For 9 cows, 13 kg 500 g of food supplement are required every day. In the same proportion, how much will be needed for 12 cows ?

Answer

Let the food supplement required for 12 cows be $x kg$.
The quantity of food supplement required and the number of cows are in direct proportion.
$
\begin{aligned}
& \therefore \frac{13 kg 500 gram }{9}=\frac{x kg }{12} \\
& \therefore \frac{13.5}{9}=\frac{x}{12} \ldots .(13 kg 500 \text { gram }=13.5 kg ) \\
& \therefore 13.5 \times 12=9 x \ldots .(\text { Multiplying both sides by } 9 \times 12) \\
& \therefore \frac{13.5 \times 12}{9}=x \\
& \therefore x=18
\end{aligned}
$
$\therefore$ The food supplement required for 12 cows is $18 kg$.

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Question 83 Marks

If Rs 600 buy 15 bunches of feed, how many will Rs 1280 buy ?

Answer

Let the bunches of feed bought for Rs 1280 be $x$.
The quantity of feed bought and their cost are in direct proportion.
$
\begin{aligned}
& \therefore \frac{600}{15}=\frac{1280}{x} \\
& \therefore 600 x =1280 \times 15 \ldots \text { (Multiplying both sides by } 15 x \text { ) } \\
& \therefore x=\frac{1280 \times 15}{600}=32
\end{aligned}
$
$\therefore 32$ bunches of feed can be bought for Rs 1280 .

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Question 93 Marks

If 7 kg onions cost Rs 140, how much must we pay for 12 kg onions ?

Answer

Let the cost of $12 kg$ onions be Rs $x$.
The quantity of onions and their cost are in direct proportion.
$
\begin{aligned}
& \therefore \frac{7}{140}=\frac{12}{x} \\
& \therefore 7 x =12 \times 140 \ldots \text { (Multiplying both sides by } 140 x \text { ) } \\
& \therefore x =\frac{12 \times 140}{7} \\
& =240
\end{aligned}
$
We must pay Rs 240 for $12 kg$ onions.

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