**OBJECTIVE QUESTIONS**

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

**QUESTION – 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 = \(\frac{17.1}{4.5}\times 12\)

**QUESTION – 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 \(\frac{8.8}{0.8}\times 80.5\)

**QUESTION – 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 = \(\frac{5}{20}\times 50\)

Hence, Raghu will cover a distance of 12.5 km in 50 minutes.

Thus, the correct option is (c).

**QUESTION – 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 = \(\frac{24\times 500}{800}\)

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

Thus, the correct option is (d).

**QUESTION – 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 = \(\frac{5}{4}\times \frac{1}{5}=\frac{1}{4}min\)

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

Thus, the correct option is (b).

**QUESTION – 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 – 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 = \(\frac{6}{4}\times 50\)

**QUESTION – 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 \(\frac{8\times 40}{10}\)

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

The correct option is (b).

**QUESTION – 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 = \(\frac{30\times 16}{20}\)

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

The correct option is (b).

**QUESTION – 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 = \(\frac{24\times 10}{8}\)

Hence, it will take 30 minutes to fill the tank if two pipes go out of order.

The correct option is (c).

**QUESTION – 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\(\frac{108}{72}\times 132\)

Hence, 132 eggs will cost Rs 198.

The correct option is (d).

**QUESTION – 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 = \(\frac{4\times 12}{15}\)

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

The correct option is (b).

**QUESTION – 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 \(\frac{24\times 500}{800}\)

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

The correct option is (a).

**QUESTION – 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 = \(\frac{140\times 14}{20}\)

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

**QUESTION – 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 \(7\frac{1}{3}h\)

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

The correct option is (d).

**QUESTION – 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 – 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 = \(\frac{10\times 8}{\frac{1}{2}}\)

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

The correct option is (d).’