# RS Aggarwal Class 7 Solutions Chapter 9 - Unitary Method Ex 9A(9.1)

## RS Aggarwal Class 7 Chapter 9 - Unitary Method Ex 9A(9.1) Solutions Free PDF

OBJECTIVE QUESTIONS

Mark () against the correct answer in each of the following:

QUESTION â€“ 1: 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

Solution:

(c) 45.6 kg

Weight of the rod of length 4.5 m = 17.1 kg

Weight of the rod of length 1 m = 17.1/4.5 kg [less length, less weight]

Therefore, Weight of the rod of length 12 m = $\frac{17.1}{4.5}\times 12$ = 45.6 kg [more length, more weight]

QUESTION â€“ 2: 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 these1

Solution:

(d) None of these

0.8 cm represents 8.8 km.

1 cm represents 8.8/0.8 km.

80.5 cm represents $\frac{8.8}{0.8}\times 80.5$ = 885.5 km.

QUESTION â€“ 3: 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

Solution:

Distance covered in 20 min = 5 km

Distance covered in 1 min = 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 â€“ 4: 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

Solution:

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

Number of days for which 1 man has enough food = 24 x 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 â€“ 5: 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

Solution:

Time taken to fill 4/5 of a cistern = 1 min

Time taken to fill 1 cistern = 5/4 min

Time taken to fill 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).

QUESTION â€“ 6: 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

Solution:

Number of cows that eat as much as 15 buffaloes = 21

Number of cows that eat as much as 1 buffalo = 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 â€“ 7: A tree, 6 m, casts a 4 m long shadow. At the same time 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

Solution:

(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 = 6/4 m

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

QUESTION â€“ 8: 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

Solution:

8 men can finish the work in 40 days.

1 man can finish the work in 8 x 40 days. [less men, more days]

10 men can finish the work in $\frac{8\times 40}{10}$ = 32 days. [more men, less days]

Therefore, If 2 more men join them, the work will be completed in 32 days.

The correct option is (b).

QUESTION â€“ 9: 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

Solution:

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 x 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 â€“ 10: 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

Solution:

Time taken to fill the tank by 10 pipes = 24 min

Time taken to fill the tank by 1 pipe = 24 x 10 [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 â€“ 11: 6 dozen eggs are bought for Rs 108. How much will 132 eggs cost?

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

Solution:

Cost of 72 eggs = Rs 108

Cost of 1 egg = Rs 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 â€“ 12: 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) 2 hrs 30 min

Solution:

Time taken by 12 workers to complete the job = 4 h

Time taken by 1 worker to complete the job = 4 x 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 â€“ 13: 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

Solution:

500 men had enough food for 24 days.

1 man had enough food for 24 x 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 â€“ 14: A rope makes 140 rounds of the circumference of a cylinder, the radius of those 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

Hint. Let the required number of rounds be x.

More radius of the cylinder, less is the number of rounds.

Therefore, $\: 20:14::140:x$. Find x.

Solution:

(c) 98

No. of rounds around the cylinder of radius 14 cm = 140

No. of rounds around the cylinder of radius 1 cm = 140 x 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 â€“ 15: A worker makes a toy $\frac{2}{3}$ 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

Solution:

No. of toys made in 2/3 h = 1

No. of toys made in 1 h = 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 â€“ 16: 10 men can finish the construction of a wall in 8 days. How many men are added to finish the work in half a day?

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

Hint. Let x men can finish the work in $\frac{1}{2}$ day. Then, less days, more men required (indirect).

Therefore, $\:\frac{1}{2}:8::10:x$. Find x = 160.

Number of men to be added = (160 â€“ 10) = 150.

Solution:

Men required to finish the work in 8 days = 10

Men required to finish the work in 1 day = 10 x 8 [More days, less men]

Men required to finish the work in half a day = $\frac{10\times 8}{\frac{1}{2}}$ = 10 x 8 x 2 = 160 [Less days, more men]

Hence, 150 (i.e., 160 â€“ 10) men are added to finish the work in half a day.

The correct option is (d).’

#### Practise This Question

Photosynthesis can be described in terms of matter and energy. Which of the following options best describes the transformations of matter and energy in photosynthesis?