# Chain Rule

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## Basic Concept of Chain Rule

Work done depends upon various parameters like number of people who are working, hours per day for which they work, the number of days for which they work and in some cases on the parameter of efficiency also.
Work ∝ n          ----1 where n is the number of people who are working.

Work ∝ d          ----2 where d is the number of days.
Merging equation 1 and equation 2
Work ∝ nd
Work = knd , where k is the constant of proportionality

So, based upon the parameters that are specified in the question we have to use one of the formulas specified below.
Work = k(Men)(Days), if men and days are given
Work = k(Men)(Hours), if men and hours are given
Work = k(Men)(Days)(Hours), if men, days and hours are given

### SHORTCUT:

If the entire work is done in 'n' days, then 1/n of the work is done in a day.

### NOTE:

If one parameter becomes n times, then other parameter becomes 1/n times.

### FORMULA: where W is the work, M is the number of men, H are the number of hours and D are the number of days. If any of the above mentioned parameter is not given in the question then leave that parameter.

Q1) If 4 pencils cost Rs 15, then find the cost of 10 pencils.
1) 37.5
2) 30
3) 25
4) None of these

Solution:

4 pencils = Rs 15
1 pencil = Rs 15/4
10 pencils = Rs (15×10)/4 = Rs 37.5
Hence, option 1.

Q2) A car travels 11.25 Km in 750 ml of fuel, what is the cost to travel 63.75 Km given that 1 liter of fuel costs Rs 61?
1) Rs 258
2) Rs 259.25
3) Rs 260
4) Rs 315

Solution:

To travel 11.25 Km fuel required = .75 liter
Distance travelled in 1 Liter of fuel = 11.25/(.75) Km = 15 Km
Car travels 15 Km in 1 liter of fuel.
Fuel required to travel 63.75 Km = 63.75/15 liters = 4.25 liters
Cost of 4.25 liters of fuel = 4.25×61 = Rs 259.25
Hence, option 2.

Q3) If 2/5th of a work is completed in 6 days. At this rate, how many more days will it takes to finish the work?
1) 9 days
2) 15 days
3) 12 days
4) None of these

Solution:

As 2/5 of a work is done in 6 days therefore, 2W/5 = 6
On solving, W = 15 i.e. Work (W) is completed in 15 days.
More days required to finish the work = 15 – 6 = 9 days
Hence, option 1.

Q4) A hostel had provision for 240 girls for a few days. After 10 days 48 girls joined the hostel and the provision lasts for 15 days?
1) 22 days
2) 36 days
3) 42 days
4) 28 days

Solution:

Say the hostel had a provision for y days
Total Food Available = Food consumed by 240 girls in 10 days + Food concumed by 240 + 48 additional girls in 15 days
240y = 240×10 + (240 + 48)×15
On solving, y = 28 days
Hence, option 4.