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- Question
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Options- A. 648
- B. 1800
- C. 2700
- D. 10800
- Correct Answer
- 1800
Explanation
Let the required number of bottles be xMore machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines 6 : 10 ] :: 270 : x Time (in minutes) 1 : 4 ∴ 6 x 1 x x = 10 x 4 x 270
⟹ x = (10 x 4 x 270) (6) ⟹ x = 1800.
- 1. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
Options- A. Rs. (xy⁄d)
- B. Rs. (xd)
- C. Rs. (yd)
- D. Rs. (yd⁄x) Discuss
- 2. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Options- A. 4
- B. 9
- C. 12
- D. 49 Discuss
- 3. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Options- A. 20
- B. 30
- C. 40
- D. 50 Discuss
- 4. If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
Options- A. 1
- B. 7⁄2
- C. 7
- D. 49 Discuss
- 5. An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth?
Options- A. 178
- B. 195
- C. 204
- D. 488 Discuss
- 6. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
Options- A. 48 paise
- B. 54 paise
- C. 56 paise
- D. 72 paise Discuss
- 7. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options- A. 29 1⁄5
- B. 37 1⁄4
- C. 42
- D. 54 Discuss
- 8. A man completes 5⁄8 of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
Options- A. 5
- B. 6
- C. 7
- D. 7 1⁄2 Discuss
- 9. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options- A. 10
- B. 13
- C. 14
- D. 15 Discuss
- 10. A man can row three-quarters of a kilometre against the stream in 11¼ minutes and down the stream in 7½ minutes. The speed (in km/hr) of the man in still water is:
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
Chain Rule problems
Search Results
Correct Answer: Rs. (yd⁄x)
Explanation:
Cost of x metres = Rs. d.
| Cost of 1 metre = Rs. | ❨ | d | ❩ |
| x |
| Cost of y metres = Rs. | ❨ | d | . y | ❩ | = Rs. | ❨ | yd | ❩. |
| x | x |
Correct Answer: 9
Explanation:
Let the required number of revolutions made by larger wheel be x
Then, More cogs, Less revolutions (Indirect Proportion)
∴ 14 : 6 :: 21 : x ⟺ 14 x x = 6 x 21
| ⟹ x = | 6 x 21 |
| 14 |
⟹ x = 9.
Correct Answer: 30
Explanation:
There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children ≡ 120 men.
| 50 children ≡ | ❨ | 120 | x 50 | ❩ | = 30 men. |
| 200 |
Correct Answer: 7
Explanation:
Let the required number days be x
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
| Spiders | 1 | : | 7 | ] | :: 7 : x |
| Webs | 7 | : | 1 |
∴ 1 x 7 x x = 7 x 1 x 7
⟹ x = 7.
Correct Answer: 195
Explanation:
Let the required time be x seconds.
More metres, More time (Direct Proportion)
∴ 0.128 : 25 :: 1 : x ⟺ 0.128x = 25 x 1
| x = | 25 | = | 25 x 1000 |
| 0.128 | 128 |
⟹ x = 195.31.
∴ Required time = 195 sec (approximately).
Correct Answer: 48 paise
Explanation:
Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
∴ 250 : 200 :: 60 : x ⟺ 250 x x = (200 x 60)
| ⟹ x= | (200 x 60) |
| 250 |
⟹ x = 48.
Correct Answer: 42
Explanation:
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
∴ 125 : 150 :: 35 : x ⟺ 125 x x = 150 x 35
| ⟹ x = | 150 x 35 |
| 125 |
⟹ x = 42.
Correct Answer: 6
Explanation:
| Work done = | 5 |
| 8 |
| Balance work = | ❨ | 1 - | 5 | ❩ | = | 3 |
| 8 | 8 |
Let the required number of days be x.
| Then, | 5 | : | 3 | = :: 10 : x | ⟺ | 5 | x x = | 3 | x 10 |
| 8 | 8 | 8 | 8 |
| ⟹ x = | ❨ | 3 | x 10 x | 8 | ❩ |
| 8 | 5 |
⟹ x = 6.
Correct Answer: 13
Explanation:
Let the required number of days be x
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
| Persons | 30 | : | 39 | ] | :: 12 : x |
| Working hours/day | 6 | : | 5 |
∴ 30 x 6 x x = 39 x 5 x 12
| ⟹ x = | (39 x 5 x 12) |
| (30 x 6) |
⟹ x = 13.
Correct Answer: 5
Explanation:
We can write three-quarters of a kilometre as 750 metres,
and 11¼ minutes as 675 seconds.
| Rate upstream = | ❨ | 750 | ❩m/sec | = | 10 | m/sec. |
| 675 | 9 |
| Rate downstream = | ❨ | 750 | ❩m/sec | = | 5 | m/sec. |
| 450 | 3 |
| ∴ Rate in still water = | 1 | ❨ | 10 | + | 5 | ❩m/sec |
| 2 | 9 | 3 |
| = | 25 | m/sec |
| 18 |
| = | ❨ | 25 | x | 18 | ❩km/hr |
| 18 | 5 |
= 5 km/hr.
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