15 men could finish a piece of work in 210 days. But at the end of 100 days, 15 additional menare employed. In how many more days will the work be complete?a)80 daysb)60 daysc)55 daysd)50 daysCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Try understand in simple way.

total time 210 . and working days 100.
and remaining day 110
so 100 days work by15 ᎷᎯᏁ
•and remaining days 110 may be 15 .
•but suddenly add 15 so total 30 person .now you can say 15 person work in 110 days and 30 person 110×15/30=55 ans...

Answer

Answer

15 Men 1 day Work=1/210
15 Men 100 day Work=1/210*100
=10/21
Remaining Work= 11/21
Now, 15 more men were added.So,total no.of men=30
30 Men 1 day Work=2/210=1/105
1/105*d=11/21,( where d= more no.of days req. to complete remaining Work)
d=55days

Answer

Given:
- 15 men can finish a piece of work in 210 days.
- 15 additional men are employed after 100 days.

To find: In how many more days will the work be complete?

Approach:
- Let's assume that the total work is 1 unit.
- We can use the formula:
- Work = Rate x Time
- Total work = Sum of individual works
- Using the above formula, we can find the rate of work of each man.

Solution:
- Let the rate of work of each man be R.
- Total work = 1 unit
- Total men = 15
- Time taken by 15 men to complete the work = 210 days
- Work done by 15 men in 1 day = R * 15
- Work done by 15 men in 210 days = 1 unit
- So, we can write: R * 15 * 210 = 1
- Solving for R, we get: R = 1 / (15 * 210)

- After 100 days, 15 more men are employed.
- So, the total men working on the project = 30
- Let the time taken by them to complete the remaining work be 't' days.
- Work done by the first 15 men in 100 days = R * 15 * 100
- Work remaining after 100 days = 1 - (R * 15 * 100)
- Work done by 30 men in 't' days = R * 30 * t
- Total work done = Work done by first 15 men + Work done by next 15 men
- Total work done = R * 15 * 100 + R * 30 * t
- Total work done = R * 15 * 100 + R * 30 * t
- Total work done = R * 15 * (100 + 60 * t)
- Total work done = (1 / (15 * 210)) * 15 * (100 + 60 * t)
- Total work done = (100 + 60 * t) / 210

- As the total work done is equal to 1 unit, we can write:
- (100 + 60 * t) / 210 = 1
- 100 + 60 * t = 210
- 60 * t = 110
- t = 110 / 60
- t = 1.83 days

- Therefore, the work will be completed in 100 + 1.83 = 101.83 days.
- Rounding off to nearest integer, we get 102 days.
- Hence, the correct option is (c) 55 days.

Note:
- In this solution, we have assumed that the rate of work of each man remains constant throughout the project.
- In reality, the rate of work may vary due to various reasons such as fatigue, illness, etc.

Answer

Step 1 - find time required for 1 man to complete the work

T1 = 210 ÷ 15 = 14 days (Time required for 1 man to complete the task)

Step 2 - find how fast can two men complete the same work

If one man can complete task in 14 days, then 2 men can do it in
T2 = 14 ÷ 2 = 7 days

Step 3 - To find the new number of days to complete the work Cross multiply the remaining days with T1 and T2

N1 = 210 - 100 = 110 days,
N2 = ?

T1/T2 = N1/N2;

14/7 = 110/N2

N2 = (110 × 7)/14 => 55 days

Answer

Simply make a linear expression for it , otherwise it will take
time in exam

15×210 = 15×100 + 30× D

D=55

explanation - total work(15 men for 210 days ) = 15 men did it for 100 days and an additional 15men (total 30) after 100 days , let say they will take another D days to complete .

Answer

15 men did 100 days work remaining days work is 110 day
now if we add 15 more men i.e we double it then the time 110 days must be also halves because days and number of workers are inversely related so if 15 men required 110 days so 30 men i.e 2*15 men requires 110/2 = 55 days. correct me if my logic is wrong and upvot me if you find this helpful.

Answer

(15x210-15x100)/30=55

Answer

30 men have the power to do it in 105 days, half of 210 as we consider all men have same working rate in a day. 15 men with power of doing 100% work in 210 days, have done (100/210)*100% of work. Remaining work should be done at twice pace. 30 men do 100% in 105 days, then do remaining % in how many days with twice pace i.e (210-100) = 110 at pace of 2x => 110/2 = 55 days sufficient.

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