Unitary Method problems
- 1. If in a hostel 45 days, food is available food is available for 50 students, for how many days will this food be sufficient for 75 students?
Options- A. 25 days
- B. 28 days
- C. 30 days
- D. 40 days Discuss
Correct Answer: 30 days
Explanation:
For 50 students, food is sufficient for 45 days
? For 1 student, food is sufficient for 45 x 50 days
and for 75 students, food is sufficient for (45 x 50)/75 days. i,e., for 30 days.
- 2. If price of m articles is ? n, then what is the price of 5 articles?
Options- A. ? 5n/m
- B. ? mn/5
- C. ?m/n
- D. ? 5m/n Discuss
Correct Answer: ? 5n/m
Explanation:
? Price of m articles = ? n
? Price of 1 article = ? n/m
? Price of 5 articles = ? 5n/m
- 3. 12 men can do a piece of work in 24 days. How many days are needed to complete the work, if 8 men are engaged in the same work?
Options- A. 28
- B. 36
- C. 48
- D. 52 Discuss
Correct Answer: 36
Explanation:
Let the required number of days be N.
Let men, More days (indirect proportion)
8 : 12 : : 24 : N
? N = (12 x 24)/8 = 36 days
- 4. Maganlal, a worker, makes an article in every 2/3h. If he works for 7 1/ 2h, then how many articles will he make?
Options- A. 111/4
- B. 111/3
- C. 112/6
- D. 112/5 Discuss
Correct Answer: 111/4
Explanation:
? In 2/3h, 1 article is made.
? In 1h, 3/2 article are made.
? In 71/2 = 15/2h, 3/2 x 15/2 = 45/4 article are made.
? Required articles = 45/4 = 112/4
- 5. Shantanu completes 5/8 of a job in 20 days. At this rate, how many more days will he take to finish the job?
Options- A. 6 days
- B. 18 days
- C. 5 days
- D. 12 days Discuss
Correct Answer: 12 days
Explanation:
Let the required number of days be N.
Remaining work = 1 - 5/8 = 3/8
Less work, Less days (Direct proportion)
5/8 : 3/8 : : 20 : N
? N = (3/8) x 20 x 8/5
? N = 12 days
- 6. 20 men can build 56 m long wall in 6 days. What length of a similar wall can be built by 70 men in 3 days?
Options- A. 100 m
- B. 98 m
- C. 48 m
- D. 85 m Discuss
Correct Answer: 98 m
Explanation:
Let the required length be L m.
More men, More length (Direct proportion)
Less days, Less length (Direct proportion)
Men 20 : 70
Days 6 : 3
? (20 x 6 x L) = (70 x 3 x 56)
? L = (70 x 3 x 56) / (20 x 6) = 98 m
- 7. 22 men can complete a job in 16 days. In how many days, will 32 men complete that job?
Options- A. 14
- B. 12
- C. 16
- D. None of these Discuss
Correct Answer: None of these
Explanation:
? 22 men do the work in 16 days.
? 1 man will do the work in 16 x 22 days.
? 32 men will do the job in = (16 x 22)/32 days
? Required number of days = (16 x 22)/32 = 11 days
- 8. If 30 men working 9 h per day can reap a field in 16 days, in how many days, will 36 men reap the field working 8 h per day?
Options- A. 15
- B. 25
- C. 18
- D. 10 Discuss
Correct Answer: 15
Explanation:
Here M1 = 30, D1 = 16,
T1 = 9, M2 = 36 and T2 = 8
By formula, M1D1T1 = M2D2T2
30 x 16 x 9 = 36 x D2 x 8
? D2 = (30 x 16 x 9)/(36 x 8) = 15 days
- 9. A garrison of 1000 men had provisions for 48 days. However, a reinforcement of 600 men arrived. How long will now food last for?
Options- A. 35 days
- B. 30 days
- C. 25 days
- D. 45 days Discuss
Correct Answer: 30 days
Explanation:
? For 1000 men, provision lasts for 48 days.
? For 1 men, provision lasts for (48 x 1000) days.
? For (1000 + 600) men, provision will last for (48 x 1000)/1600 days.
? Required number of days = (48 x 1000)/1600 = 3 x 10 = 30
- 10. If 12 persons working 16 h per day earn ? 33600 per week, then how much will 18 persons earn working 12 h per day?
Options- A. ? 40000
- B. ? 35000
- C. ? 28800
- D. ? 37800 Discuss
Correct Answer: ? 37800
Explanation:
M1 = 12 H1 = 16, W1 = 33600
M2 = 18, H2 = 12, W2 = ?
By formula, M1H1/W1 = M2H2/W2
(12 x 16)/33600 = (18 x 12)/W2
? W2 = (33600 x 18)/16
? W2 = 2100 x 8
? W2 = 37800
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