RS Aggarwal 2019,2020 solution class 7 chapter 9 Unitary Method Exercise 9B

Exercise 9B

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Question 1:

If 48 men can dig a trench in 14 days, how long will 28 men take to dig a similar trench?

Answer 1:

48 men can dig a trench in 14 days.
1 man can dig the trench in 14 $\times$ 48 days.                                               [less men, more days]
Therefore, 28 men can dig the trench in $\frac{14\times 48}{28}$ days = 24 days              [more men, less days]
Hence, 28 men will take 24 days to dig a similar trench.

Question 2:

16 men can reap a field in 30 days. How many men must be engaged to reap the same field in 24 days?

Answer 2:

No. of men required to reap the field in 30 days = 16
No. of men required to reap the field in 1 day = 16 $\times$30                        (less days, more men)
Now, no. of men required to reap the field in 24 days = $\frac{16\times 30}{24}$ = 20    (more days, less men)

∴ 20 men are required to reap the field in 24 days.

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Question 3:

45 cows can graze a field in 13 days. How many cows will graze the same field in 9 days?

Answer 3:

Number of cows that can graze the field in 13 days = 45
Number of cows that can graze the field in 1 day = 45 $\times$13           [Less days, more cows]
Therefore, number of cows that can graze the field in 9 days = $\frac{45\times 13}{9}$ = 65   [More days, less cows]

Hence, 65 cows can graze the field in 9 days.

Question 4:

16 horses can consume a certain quantity of corn in 25 days. In how many days would the same quantity be consumed by 40 horses?

Answer 4:

Time taken by 16 horses to consume the corn = 25 days
Time taken by 1 horse to consume the corn = 25$\times$16                    [less horses, more time taken]
Time taken by 40 horses to consume the corn = $\frac{25\times 16}{40}$= 10 days     [more horses, less time taken]

Hence, 40 horses would consume the same quantity of corn in 10 days.

Question 5:

A girl can finish a book in 25 days if she reads 18 pages of it every day. How many days will she take to finish it, if she reads 15 pages every day?

Answer 5:

Days taken to finish the book if 18 pages are read everyday = 25
Days taken to finish the book if 1 page is read everyday = 18 $\times$25                          [less pages, more days]
Now, days taken to finish the book if 15 pages are read everyday = $\frac{18\times 25}{15}$ = 30     [more pages, less days]
Hence, the girl will take 30 days to finish the book if she reads 15 pages everyday.

Question 6:

Reeta type 40 words per minute and takes 24 minutes to type a certain document. Her friend Geeta has a typing speed of 48 words per minute. In how much time, will she be able to type the same document?

Answer 6:

Time taken to type 40 words per minute = 24 min
Time taken to type a word per minute = 24$\times$40 min                     
Now, time taken to type 48 words per minute = $\frac{24\times 40}{48}$ = 20 min

Hence, Geeta will take 20 minutes to type the same document if her typing speed is 48 words/min.

Question 7:

A bus covers a certain distance in 3 hours 20 minutes at an average speed 45 km/h. How long will it take to cover the same distance at a speed of 36 km/h?

Answer 7:

Time taken to cover the distance at a speed of 45 km/h = 3 h 20 min = 200 min
Time taken to cover the distance at a speed of 1 km/h = 45 $\times$ 3.33 min             [less speed, more time]
Time taken to cover the distance at a speed of 36 km/h = $\frac{45\times 3.33}{36}$ = 4.1625 h ≈ 4 h 10 min

Hence, the bus will take 4 h 10 min to cover the distance if its speed is 36 km/h.

Question 8:

At the beginning of a month, a factory has enough materials to make 240 tonnes of steel in a month. If 60 more tonnes of steel is to be made that month, how long will the materials last?

Answer 8:

Time taken to make 240 tonnes of steel = 30 days
Time taken to make 1 tonne of steel = 30 $\times$ 240 days
Now, time taken to make 300 or (240 + 60) tonnes of steel = $\frac{30\times 240}{300}$ = 24 days

∴ The materials will last for 24 days if 60 more tonnes of steel is to be made that month.

Question 9:

A contractor employed 210 men to build a house in 60 days. After 12 days, he was joined by 70 more men. In how many days will the remaining work be finished?

Answer 9:

Initially, the contractor had 210 men for 60 days. After 12 days, 70 more men joined.

210 men can finish the work in 48 days
1 man can finish the work in 210$\times$48 days
Now, 280 men can finish the work in $\frac{210\times 48}{280}$ days = 36 days.

Hence, it will take 36 days to finish the remaining work.

Question 10:

A military camp has provisions for 360 men to last for 25 days. How many men must be transferred to another camp so that the food lasts for 30 days?

Answer 10:

No. of men for which the provision will last for 25 days = 360
No. of men for which the provision will last for 1 day = 360 $\times$25
Now, no. of men for which the provision will last for 30 days = $\frac{360\times 25}{30}$ = 300

∴ 60 men, i.e., (360 − 300), must be transferred to another camp so that the provision lasts for 30 days.

Question 11:

A group of 120 men had provisions for 200 days. After 5 days, 30 men died due to an epidemic. How long will the remaining food last?

Answer 11:

Number of days for which the food is sufficient for 120 men = 195
Number of days for which food is sufficient for 1 man = 120$\times$195
Number of days for which food is sufficient for 90 men = $\frac{120\times 195}{90}$ = 260

Hence, the food will last for 260 days.

Question 12:

1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were transferred to another fort and thus the food lasted for an extra 32 days. How many soldiers left the fort?

Answer 12:

We are given that in a fort, 1200 soldiers had enough food for 28 days.
Let x soldiers left after 4 days, thus, remaining soldiers = 1200 - x
Now, for these remaining soldiers food lasts for 32 days.
As number of soldiers decrease, food lasts long.

Thus, situation after 4 days is
$$\begin{gathered} 1200\times 24=\left(1200-x\right)\times 32 \\ \Rightarrow \left(1200-x\right)=\frac{1200\times 24}{32} \\ \Rightarrow 1200-x=900 \\ \Rightarrow x=1200 - 900 \\ \Rightarrow x=300 \end{gathered}$$

Thus, 300 soldiers left the fort after 4 days.