RS Aggarwal 2019,2020 solution class 7 chapter 9 Unitary Method Test Paper 9

Test Paper 9

Page-137

Question 1:

If the cost of 8 toys is Rs 192, what will be the cost of 14 such toys?

Answer 1:

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

Question 2:

A car can cover 270 km in 15 litres of petrol. How many kilometres will it cover in 8 litres of petrol?

Answer 2:

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

Question 3:

If 15 envelopes cost Rs 11.25, what is the cost of 20 such envelopes?

Answer 3:

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

Question 4:

24 cows can graze a field in 20 days. How many cows can graze it in 15 days?

Answer 4:

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]

Question 5:

8 men can finish a piece of work in 15 hours. In how many hours can 20 men finish it?

Answer 5:

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]

Question 6:

If $\frac{4}{5}$ of a cistern is filled in 1 minute, how much time will be required to fill the empty cistern?

Answer 6:

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.

Question 7:

A bus covers a certain distance in 3 hours 20 minutes at an average speed of 45 km per hour. How much time will it take to cover the same distance at a speed of 50 km per hour?

Answer 7:

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]

Question 8:

In a fort, 120 men had provisions for 30 days. For how many days is the food sufficient for 100 men?

Answer 8:

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]

Question 9:

Mark (✓) against the correct answer
In a map, 1 cm represents 8 km. How much distance will be represented by 80.5 cm?

(a) 640 km
(b) 642 km
(c) 644 km
(d) 648 km

Answer 9:

(c) 644 km
1 cm represents 8 km.
∴ 80.5 cm  represents $8\times 80.5$ = 644 km.

Question 10:

Mark (✓) against the correct answer
If 16 men can reap a field in 30 days, in how many days will 20 men reap the same field?

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

Answer 10:

(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]

Question 11:

Mark (✓) against the correct answer
If 21 cows eat as much as 15 buffaloes, how many cows will eat as much as 35 buffaloes?

(a) 45
(b) 49
(c) 56
(d) 54

Answer 11:

(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

Question 12:

Mark (✓) against the correct answer
45 cows can graze a field in 12 days. How many cows will graze the same field in 9 days?

(a) 60 days
(b) $38\frac{3}{4}$ days
(c) 54 days
(d) none of these

Answer 12:

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

Question 13:

Mark (✓) against the correct answer
6 dozen eggs are bought for Rs 108. How much will 108 eggs cost?

(a) Rs 171
(b) Rs 162
(c) Rs 153
(d) Rs 180

Answer 13:

(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

Question 14:

Fill in the blanks.

(i) If 42 men can dig a trench in 14 days, then 1 man can dig it in ...... days.
(ii) If 15 oranges cost Rs 60, then 12 oranges cost Rs ...... .
(iii) If 10 metres of a uniform rod weighs 18 kg, then the weight of 6 metres of the rod is ...... kg.
(iv) If 12 workers finish a piece of work in 4 hours, then 15 workers will finish it in ..... hrs ..... min.

Answer 14:

(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

Question 15:

Write 'T' for true and 'F' for false

(i) If 10 pipes of the same diameter can fill a tank in 24 minutes, then 8 pipes would fill it in 19 min 20 sec.
(ii) If 8 men can finish a piece of work in 40 days, then 10 men can finish it in 32 days.
(iii) A tree 6 m tall casts a shadow of length 4 m. At the same time a flag casts a shadow of length 50 m. The lenght of the pole is 75 m.
(iv) If a worker takes $\frac{2}{3}$ hour to make a toy, then he will make 12 toys in 8 hours.

Answer 15:

(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)