Chain Rule problems
- 1. A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?
Options- A. 3
- B. 5
- C. 6
- D. 9 Discuss
Correct Answer: 5
Explanation:
[(100 x 35) + (200 x 5)]men can finish the work in 1 day
Therefore, 4500 men can finish the work in 1 day. 100 men can finish it in 4500/100= 45 days.
This is 5 days behind Schedule
- 2. If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days?
Options- A. 22
- B. 14
- C. 13
- D. 11 Discuss
Correct Answer: 11
Explanation:
Let the required no of binders be X.
Less books , Less binders (Direct Proportion)
More days, Less binders (Indirect proportion)
Therefore, (900 * 12 * x) = (660 * 10 * 18)
=> x = 11
- 3. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
Options- A. 24 days
- B. 28 days
- C. 34 days
- D. 35 days Discuss
Correct Answer: 24 days
Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x then,
27 : 36 :: 18 : x
[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
=>27x = 36 * 18
=> x = 24
So 24 days will be required to get work done by 27 men.
- 4. If a quarter kg of carrots costs 60 paise, how many paise will 200 gms cost ?
Options- A. 78 paise
- B. 48 paise
- C. 54 paise
- D. 62 paise Discuss
Correct Answer: 48 paise
Explanation:
Quarter of Kg means 250 gm
Less weight, less price (Direct Proportion)
So,
250 : 200 :: 60 : x => x = 48
So 200 gm will cost 48 paise.
- 5. The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero ?
Options- A. 14th element
- B. 9th element
- C. 12th element
- D. 7th element Discuss
Correct Answer: 12th element
Explanation:
If we consider the third term to be ?x?
The 15th term will be (x + 12d)
6th term will be (x + 3d)
11th term will be (x + 8d) and
13th term will be (x + 10d).
Thus, as per the given condition, 2x + 12d = 3x + 21d.Or x + 9d = 0.
x + 9d will be the 12th term.
Thus, 12th term of the A.P will be zero.
- 6. Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in
Options- A. 6 days
- B. 12 days
- C. 4 days
- D. 3 days Discuss
Correct Answer: 3 days
Explanation:
Let x men can do the in 12 days and the required number of days be z
More men, Less days [Indirect Proportion]
Less work, Less days [Direct Proportion ]
- 7. In a queue, Shankar is ninth from the rear end. Althaf's place is eighth from the front. Nitu is standing between the two. What could be the minimum numbers of boys standing in the queue ?
Options- A. 18
- B. 14
- C. 22
- D. 24 Discuss
Correct Answer: 14
Explanation:
1 2 3 4 5 6(Shankar) 7(Nitu) 8(Althaf) 9 10 11 12 13 14
Here, Althaf is 8th from front, Shankar is 9th from rear end and Nitu is between them
So minimum no. of boys standing in the queue = 14
- 8. If a person having Rs. 2000 and he want to distribute this to his five children in the manner that each son having Rs. 30 more than the younger one , what will be the share of youngest child ?
Options- A. Rs. 175
- B. Rs. 325
- C. Rs. 340
- D. Rs. 260 Discuss
Correct Answer: Rs. 340
Explanation:
Assume first child (the youngest) get = Rs. x
According to the question ;
each son having Rs. 30 more than the younger one
Second child will get = Rs. x + 30
Third child will get = Rs. x + 30 + 30 = x + 60
Forth child will get = Rs. x + 30 + 30 + 30 = x + 90
Fifth child will get = Rs. x + 30 + 30 + 30 + 30 = x + 120
Total amount they got = Rs. 2000
x + (x+30) + (x+60) + (x+90) + (x+120) = 2000
5x + 300 = 2000
5x = 1700
x = Rs. 340
So the youngest child will get Rs. 340.
- 9. If 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?
Options- A. 350
- B. 400
- C. 425
- D. 450 Discuss
Correct Answer: 450
Explanation:
Let the required no of hectares be x. Then
More men, More hectares (Direct proportion)
More days, More hectares (Direct proportion)
=> ( 8 * 24 * x) = (36 * 30 * 80)
=> x= 450
- 10. 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
- B. 37
- C. 42
- D. 54 Discuss
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
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