myhelper: RS Aggarwal 2019,2020 solution class 7 chapter 9 Unitary Method Exercise 9C

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

Exercise 9C

Page-135

Question 1:

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If 4.5 m of a uniform rod weighs 17.1 kg, what is the weight of 12 m of such a rod?

(a) 51.2 kg
(b) 53 kg
(c) 45.6 kg
(d) 56 kg

Answer 1:

\frac{17.1}{4.5}

kg [less length, less weight]

∴ Weight of the rod of length 12 m =

\frac{17.1}{4.5} \times 12

= 45.6 kg [more length, more weight]

Question 2:

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In a map, 0.8 cm represents 8.8 km. How much distance will be represented by 80.5 cm?

(a) 805 km
(b) 855.5 km
(c) 644 km
(d) none of these

Answer 2:

(d) none of these

0.8 cm represents 8.8 km.

1 cm represents

\frac{8.8}{0.8}

km.

80.5 cm represents

\frac{8.8}{0.8} \times 80.5

= 885.5 km.

Question 3:

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In a race, Raghu covers 5 km in 20 minutes, how much distance will he cover in 50 minutes?

(a) 10.5 km
(b) 12 km
(c) 12.5 km
(d) 13.5 km

Answer 3:

Distance covered in 20 min = 5 km
Distance covered in 1 min =

\frac{5}{20}

km [less time, less distance covered]
Distance covered in 50 min =

\frac{5}{20} \times 50

= 12.5 km [more time, more distance covered]
Hence, Raghu will cover a distance of 12.5 km in 50 minutes.

Thus, the correct option is (c).

Question 4:

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A garrison of 500 men had provisions for 24 days. However, a reinforcement of 300 men arrived. The food will now last for

(a) 18 days
(b)

17 \frac{1}{2}

days
(c) 16 days
(d) 15 days

Answer 4:

Number of days for which 500 men have enough food = 24
Number of days for which 1 man has enough food = 24

\times

500 [less men, more food]
Number of days for which 800 men have enough food =

\frac{24 \times 500}{800}

= 15 [more men, less food]
Hence, the food will last for 15 days after the reinforcement of 300 men.

Thus, the correct option is (d).

Question 5:

Mark (✓) against the correct answer
If

\frac{4}{5}

of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it?

(a) 20 seconds
(b) 15 seconds
(c) 12 seconds
(d) 10 seconds

Answer 5:

Time taken to fill

\frac{4}{5}

of a cistern = 1 min
Time taken to fill 1 cistern

= \frac{5}{4}

min
Time taken to fill

\frac{1}{5}

of a cistern =

\frac{5}{4} \times \frac{1}{5} = \frac{1}{4}

min = 15 seconds

Hence, it will take 15 seconds to fill the rest of the cistern.

Thus, the correct option is (b).

Page-136

Question 6:

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If 21 cows eat as much as 15 buffaloes, how many cows will eat as much as 35 buffaloes?

(a) 49
(b) 56
(c) 45
(d) none of these

Answer 6:

Number of cows that eat as much as 15 buffaloes = 21
Number of cows that eat as much as 1 Buffalo = $\frac{21}{15}$
Number of cows that eat as much as 35 buffaloes = $\frac{21}{15} \times 35$ = 49
Hence, 49 cows will eat as much as 35 buffaloes.

Thus, the correct option is (a).

Question 7:

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A tree, 6 m tall, casts a 4-m-long shadow. At the same a flag pole casts a 50-m-long shadow. How long is the flag pole?

(a) 50 m
(b) 75 m
(c) $33 \frac{1}{3} m$
(d) none of these

Answer 7:

(b) 75 m

Height of the tree that casts a 4 m long shadow = 6 m
Height of the tree that casts a 1 m long shadow = $\frac{6}{4}$ m
∴ Height of the flag pole that casts a 50 m long shadow = $\frac{6}{4} \times 50$ = 75 m

Question 8:

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8 men can finish a piece of work in 40 days. If 2 more men join them, the work will be completed in

(a) 30 days
(b) 32 days
(c) 36 days
(d) 25 days

Answer 8:

8 men finish the work in 40 days.
1 man can finish the work in 8 $\times$ 40 days. [Less men, more days]
10 men can finish the work in $\frac{8 \times 40}{10}$ = 32 days. [More men, less days]
∴ If 2 more men join them, the work will be completed in 32 days.

The correct option is (b).

Question 9:

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If 16 men can reap a field in 30 days, in how many days will 20 men reap the same field?

(a) $10 \frac{2}{3}$ days
(b) 24 days
(c) 25 days
(d) $37 \frac{1}{2}$ days

Answer 9:

Number of days taken to reap the field by 16 men = 30 days
Number of days taken to reap the field by 1 man = 30 $\times$ 16 days [Less men, more days]
Number of days taken to reap the field by 20 men = $\frac{30 \times 16}{20}$ = 24 days [More men, less days]

Hence, 20 men will take 24 days to reap the field.

The correct option is (b).

Question 10:

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10 pipes of the same diameter can fill a tank in 24 minutes. If 2 pipes go out of order, how long will the remaining pipe take to fill the tank?

(a) 40 min
(b) 45 min
(c) 30 min
(d) $19 \frac{1}{5}$ min

Answer 10:

Time taken to fill the tank by 10 pipes = 24 min
Time taken to fill the tank by 1 pipe = 24 $\times$ 10 min [Less pipes, more time taken]
Time taken to fill the tank by 8 pipes = $\frac{24 \times 10}{8}$ min = 30 min [More pipes, less time taken]
Hence, it will take 30 minutes to fill the tank if two pipes go out of order.

The correct option is (c).

Question 11:

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6 dozen eggs are bought Rs 108. How much will 132 eggs cost?

(a) Rs 204
(b) Rs 264
(c) Rs 184
(d) Rs 198

Answer 11:

Cost of 72 eggs = Rs 108
Cost of 1 egg = Rs $\frac{108}{72}$
Cost of 132 eggs = RS $\frac{108}{72} \times 132$ = Rs 198

Hence, 132 eggs will cost Rs 198.

The correct option is (d).

Question 12:

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12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?

(a) 2 hrs 40 min
(b) 3 hrs 12 min
(c) 3 hrs 24 min
(d) 3 hrs 30 min

Answer 12:

Time taken by 12 workers to complete the job = 4 h
Time taken by 1 worker to complete the job = $4 \times 12$ h
Time taken by 15 workers to complete the job = $\frac{4 \times 12}{15}$ = 3 h 12 min

Hence, 15 workers will complete the job in 3 h 12 min.

The correct option is (b).

Question 13:

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A garrison of 500 men had provisions for 27 days. After 3 days, a reinforcement of 300 men arrived. The remaining food will now last for how many days?

(a) 15 days
(b) 16 days
(c) $17 \frac{1}{2}$ days
(d) 18 days

Answer 13:

500 men had enough food for 24 days.
1 man had enough food for 24 $\times$ 500 days. [Less men, more days]
800 men had enough food for $\frac{24 \times 500}{800}$ = 15 days [More men , less days]

Hence, the food will now last for 15 days after the reinforcement of 300 men.

The correct option is (a).

Question 14:

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A rope makes 140 rounds of the circumference of a cylinder, the radius of whose base is 14 cm. How many times can it go round a cylinder with radius 20 cm?

(a) 28
(b) 17
(c) 98
(d) 200

Answer 14:

(c) 98

No. of rounds around the cylinder of radius 14 cm = 140
No. of rounds around the cylinder of radius 1 cm = $140 \times 14$ [Less radius, more rounds]
No. of rounds around the cylinder of radius 20 cm = $\frac{140 \times 14}{20}$ = 98 [More radius, less rounds]

Hence, the rope makes 98 rounds around the circumference of the cylinder of radius 20 cm.

Question 15:

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A worker makes a toy every $\frac{2}{3}$ hour. If he works for $7 \frac{1}{3}$ hours, then how many toys will he make?

(a) 22
(b) 18
(c) 16
(d) 11

Answer 15:

No. of toys made in $\frac{2}{3}$ h = 1
No. of toys made in 1 h = $\frac{3}{2}$
No. of toys made in $7 \frac{1}{3}$ h = $\frac{3}{2} \times \frac{22}{3} = 11$

Hence, the worker will make 11 toys in $7 \frac{1}{3}$ h.

The correct option is (d).

Question 16:

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10 men can finish the construction of a wall in 8 days. How meny men are added to finish the work in half a day?

(a) 160
(b) 100
(c) 120
(d) 150

Answer 16:

Men required to finish the work in 8 days = 10
Men required to finish the work in 1 day = 10 $\times$ 8 [More day, less men]
Men required to finish the work in half a day = $\frac{10 \times 8}{\frac{1}{2}} = 10 \times 8 \times 2$ = 160 [Less days, more men]
Hence, 150 (i.e., 160 − 10) men are added to finish the work in half a day.

The correct option is (d).