Rs Aggarwal Solutions for Class 7 Math Chapter 9 Unitary Method are provided here with simple step-by-step explanations. These solutions for Unitary Method are extremely popular among Class 7 students for Math Unitary Method Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal Book of Class 7 Math Chapter 9 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s Rs Aggarwal Solutions. All Rs Aggarwal Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

#### Page No 133:

#### Answer:

Cost of 15 oranges = Rs 110

Cost of 1 orange = Rs $\frac{110}{15}$

∴ Cost of 39 oranges = Rs $\frac{110}{15}\times 39$ = Rs 286

#### Page No 133:

#### Answer:

Amount of sugar bought for Rs 260 = 8 kg

Amount of sugar bought for Re 1 = $\frac{8}{260}$ kg

Now, amount of sugar bought for Rs 877.50 = $\frac{8}{260}\times 877.50$ kg = 27 kg

∴ 27 kg of sugar can be bought for Rs 877.50.

#### Page No 133:

#### Answer:

Length of the silk purchased for Rs 6290 = 37 m

Length of the silk purchased for Re 1= $\frac{37}{6290}$ m

Now, length of the silk purchased for Rs 4,420 = $\frac{37}{6290}\times 4420$ m = 26 m

∴ 26 m of silk can be purchased for Rs 4,420.

#### Page No 133:

#### Answer:

Number of days for which a worker is paid Rs 1,110 = 6

Number of days for which a worker is paid Re 1 = $\frac{6}{1110}$ days

Now, number of days for which a worker is paid Rs 4625=$\frac{6}{1110}\times 4625$ days = 25 days

∴ The worker worked 25 days in a month.

#### Page No 133:

#### Answer:

Distance covered by the car with 42 L of petrol = 357 km

Distance covered by the car with 1 L of petrol = $\frac{357}{42}$ km [less petrol, less distance]

Now, distance covered by the car with 12 L of petrol = $\frac{357}{42}\times 12$ = 102 km [more petrol, more distance]

#### Page No 133:

#### Answer:

Cost of travelling 900 km by train = Rs 2520

Cost of travelling 1 km by train = Rs $\frac{2520}{900}$

Now, cost of travelling 360 km by train =Rs $\frac{2520}{900}\times 360$ = Rs 1008

∴ The train fare for a journey of distance 360 km is Rs 1,008.

#### Page No 133:

#### Answer:

Time taken to cover a distance of 51 km = 45 min

Time taken to cover a distance of 1 km = $\frac{45}{51}$ min

Time taken to cover distance of 221 km = $\frac{45}{51}\times 221$ min = 195 min = 3 h 15 min

∴ The train will take 3 h 15 min to cover a distance of 221 km.

#### Page No 133:

#### Answer:

Length of the iron rod that weighs 85.5 kg = 22.5 m

Length of the iron rod that weighs 1 kg = $\frac{22.5}{85.5}$ m [less weight, less length]

∴ Length of the iron rod that weighs 22.8 kg = $\frac{22.5}{85.5}\times 22.8$m = 6 m [more weight, more length]

#### Page No 133:

#### Answer:

Number of paper sheets that weighs 162 g = 6

Number of paper sheets that weighs 1 g = $\frac{6}{162}$ [less weight, less sheets]

∴ Number of paper sheets that weighs 13.5 kg = $\frac{6}{162}\times 13.5\times 1000$ = 500 [more weight, more sheets]

#### Page No 133:

#### Answer:

Number of cartons needed to pack 1152 soap bars = 8

Number of cartons needed to pack 1 soap bar = $\frac{8}{1152}$ [less number of soaps, less number of cartons needed]

Now, number of cartons needed to pack 3888 soap bars = $\frac{8}{1152}\times 3888$ = 27 [more soaps, more carton needed]

∴ 27 cartons are needed to pack 3888 soap bars.

#### Page No 133:

#### Answer:

Number of cardboards in a pile of thickness 44 mm = 16

Number of cardboards in a pile of thickness 1 mm = $\frac{16}{44}$

Number of cardboards in a pile of thickness 71.5 cm = $\frac{16}{44}\times 71.5\times 10$ = 260 [1 cm=10 mm]

∴ 260 cardboards will be there in a pile of thickness 71.5 cm.

#### Page No 133:

#### Answer:

Height of the flagstaff that casts a shadow of length 8.2 m = 7 m

Height of the building that casts a shadow of length 1 m = $\frac{7}{8.2}$ m

Height of the building that casts a shadow of length 20.5 m = $\frac{7}{8.2}\times 20.5$ m = 17.5 m

∴ The height of the required building is 17.5 m.

#### Page No 133:

#### Answer:

Number of men employed to built the 16.25 m long wall = 15

Number of men required to built a 1 m long wall = $\frac{15}{16.25}$

Number of men that should be employed to built a 26 m long wall = $\frac{15}{16.25}\times 26$ = 24

∴ 24 men should be employed to build a wall of length 26 m in a day.

#### Page No 133:

#### Answer:

Number of patients who can consume 1350 L of milk = 60

Number of patients who can consume 1 L of milk = $\frac{60}{1350}$

Now, number of patients who can consume 1710 L of milk = $\frac{60}{1350}\times 1710$ = 76

Hence, 76 patients can be accommodated in the hospital if the monthly ration of milk is raised to 1710 L.

#### Page No 133:

#### Answer:

Weight that would produce an extension of 2.8 cm = 150 g

Weight that would produce an extension of 1 cm = $\frac{150}{2.8}$ g

Weight that would produce an extension of 19.6 cm = $\frac{150}{2.8}$$\times $19.6 = 1050 g = 1 kg 50 g [1 kg = 1000 g]

∴ A weight of 1 kg 50 g would produce an extension of 19.6 cm.

#### Page No 134:

#### Answer:

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.

#### Page No 134:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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.

#### Page No 135:

#### Answer:

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

$1200\times 24=\left(1200-x\right)\times 32\phantom{\rule{0ex}{0ex}}\Rightarrow \left(1200-x\right)=\frac{1200\times 24}{32}\phantom{\rule{0ex}{0ex}}\Rightarrow 1200-x=900\phantom{\rule{0ex}{0ex}}\Rightarrow x=1200-900\phantom{\rule{0ex}{0ex}}\Rightarrow x=300$

Thus, 300 soldiers left the fort after 4 days.

#### Page No 135:

#### Answer:

(c) 45.6 kg

Weight of the rod of length 4.5 m = 17.1 kg

Weight of the rod of length 1 m = $\frac{17.1}{4.5}$ 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]

#### Page No 135:

#### Answer:

(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.

#### Page No 135:

#### Answer:

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).

#### Page No 135:

#### Answer:

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).

#### Page No 135:

#### Answer:

Time taken to fill 1

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 No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

(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

#### Page No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

(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.

#### Page No 136:

#### Answer:

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).

#### Page No 136:

#### Answer:

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 = $\frac{10\times 8}{{\displaystyle \frac{1}{2}}}=10\times 8\times 2$= 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).

#### Page No 137:

#### Answer:

Cost of 8 toys = Rs 192

Cost of 1 toy = Rs $\frac{192}{8}$ = Rs 24

∴ Cost of 14 toys = $24\times 14$ = Rs 336

#### Page No 137:

#### Answer:

Distance covered with 15 L of petrol= 270 km

Distance covered with 1 L of petrol = $\frac{270}{15}$ km

Distance covered with 8 L of petrol= $\frac{270}{15}\times 8$ km = 144 km

#### Page No 137:

#### Answer:

Cost of 15 envelopes = Rs 11.25

Cost of 1 envelope = Rs $\frac{11.25}{15}$

∴ Cost of 20 envelopes = $\frac{11.25}{15}\times 20$ = Rs 15

#### Page No 137:

#### Answer:

Number of cows that graze the field in 20 days = 24

Number of cows that graze the field in 1 day = 24$\times $20 [Less days, more cows]

∴ Number of cows that graze the field in 15 days = $\frac{24\times 20}{15}$ = 32 cows [More days, less cows]

#### Page No 137:

#### Answer:

Time taken to finish the work by 8 men = 15 h

Time taken to finish the work by 1 man = 8$\times $15 h [Less men, more time taken]

∴ Time taken to finish the work by 20 men = $\frac{8\times 15}{20}$ h = 6 h [More men, less time taken]

#### Page No 137:

#### Answer:

Time taken to fill $\frac{4}{5}$ of the cistern = 1 min

Time taken to fill 1 cistern = $\frac{1}{{\displaystyle \frac{4}{5}}}=\frac{5}{4}$= 1.25 min = 1 min 15 sec

Hence, it will take 1 min 15 sec to fill the empty cistern.

#### Page No 137:

#### Answer:

Time taken to cover the distance at a speed of 45 km/h = 3 h 20 min

Time taken to cover the distance at a speed of 1 km/h = 45 $\times $ 3.33 h [Less speed, more time taken]

(20 min = 0.33 hour)

∴ Time taken to cover the distance at a speed of 50 km/h = $\frac{45\times 3.33}{50}$h ≈ 3 h [More speed, less time taken]

#### Page No 137:

#### Answer:

Number of days with enough food for 120 men = 30

Number of days with enough food for 1 man = $30\times 120$ [Less men, more days]

∴ Number of days with enough food for 100 men = $\frac{30\times 120}{100}$ = 36 [More men, less days]

#### Page No 137:

#### Answer:

(c) 644 km

1 cm represents 8 km.

∴ 80.5 cm represents $8\times 80.5$ = 644 km.

#### Page No 137:

#### Answer:

(a) 24 days

16 men can reap the field in 30 days.

1 man can reap the field in 30$\times $16 days. [Less men, more days]

∴ 20 men can reap the field in $\frac{30\times 16}{20}$ = 24 days [More men, less days]

#### Page No 137:

#### Answer:

(b) 49

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

#### Page No 137:

#### Answer:

Number of cows that graze the field in 12 days = 45

Number of cows that graze the field in 1 day = $45\times 12$

∴ Number of cows that graze the field in 9 days = $\frac{45\times 12}{9}$ = 60

#### Page No 137:

#### Answer:

(b) Rs 162

Cost of 72 eggs = Rs 108

Cost of 1 egg =Rs $\frac{108}{72}$

Cost of 108 eggs = Rs $\frac{108\times 108}{72}$ = Rs 162

#### Page No 137:

#### Answer:

(i) 588 days

42 men can dig the trench in 14 days.

1 man can dig the trench in 14 $\times $ 42 days = 588 days

(ii) Rs. 48

15 oranges cost Rs 60.

12 oranges will cost Rs $\frac{60}{15}\times 12$ = Rs 48

(iii) 10.8 kg

A rod of length 10 m weighs 18 kg.

A rod of length 6 m will weigh $\frac{18}{10}\times 6$ = 10.8 kg

(iv) 3 h 12 min

12 workers finish the work in 4 h.

15 workers will finish the work in $\frac{4\times 12}{15}$ = 3.2 h = 3 h 12 min

#### Page No 137:

#### Answer:

(i) F

10 pipes fill the tank in 24 min.

1 pipe will fill the tank in 24 $\times $10 min. (Less pipes, more time taken)

8 pipes will fill the tank in $\frac{24\times 10}{8}$ = 30 min (More pipes, less time taken)

(ii) T

8 men finish the work in 40 days.

1 man finishes the work in 8$\times $40 days. (Less men, more days taken)

10 men will finish the work in $\frac{8\times 40}{10}$ = 32 days (More men, less days taken)

(iii) T

A 6 m tall tree casts a shadow of length 4 m.

A 1 m tall tree cast a shadow of length $\frac{4}{6}$ m.

A 75 m tall pole will cast a shadow of length $\frac{4}{6}\times 75$ =50 m

(iv) T

1 toy is made in $\frac{2}{3}$ h. (Less toys, less time taken)

12 toys can be made in $\frac{2}{3}\times 12$ = 8 h (More toys, more time taken)

View NCERT Solutions for all chapters of Class 7