Chain Rule problems
- 1. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
Options- A. 1
- B. 11⁄40
- C. 40
- D. 80 Discuss
Correct Answer: 40
Explanation:
Let the required number of days be x
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
| Cows | 1 | : | 40 | ] | :: 40 : x |
| Bags | 40 | : | 1 |
∴ 1 x 40 x x = 40 x 1 x 40
⟹ x = 40.
- 2. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Options- A. 12
- B. 18
- C. 22
- D. 24
- E. None of these Discuss
Correct Answer: 24
Explanation:
Let the required number of days be x
Less men, More days (Indirect Proportion)
∴ 27 : 36 :: 18 : x ⟺ 27 x x = 36 x 18
| ⟹ x = | 36 x 18 |
| 27 |
⟹ x = 24.
- 3. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Options- A. 9
- B. 10
- C. 11
- D. 12 Also asked in: Bank Exams, Bank PO
Correct Answer: 12
Explanation:
Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
| Pumps | 4 | : | 3 | ] | :: 8 : x |
| Days | 1 | : | 2 |
∴ 4 x 1 x x = 3 x 2 x 8
| ⟹ x = | (3 x 2 x 8) |
| (4) |
⟹ x = 12.
- 4. 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
Options- A. 4
- B. 8
- C. 12
- D. 16 Discuss
Correct Answer: 16
Explanation:
Let the required number of bottles be x
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
| Wavers | 4 | : | 8 | ] | :: 4 : x |
| Days | 4 | : | 8 |
∴ 4 x 4 x x = 8 x 8 x 4
| ⟹ x = | (8 x 8 x 4) |
| (4 x 4) |
⟹ x = 16.
- 5. A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:
Options- A. 10 m
- B. 12.5 m
- C. 17.5 m
- D. 21.25 m Discuss
Correct Answer: 12.5 m
Explanation:
Let the height of the building x metres.
Less lengthy shadow, Less in the height (Direct Proportion)
∴ 40.25 : 28.75 :: 17.5 : x ⟺ 40.25 x x = 28.75 x 17.5
| x = | 28.75 x 17.5 |
| 40.25 |
⟹ x = 12.5
- 6. 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
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).
- 7. 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
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.
- 8. 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
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 |
- 9. 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
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.
- 10. 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
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 |
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