Chain Rule
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. Download: Chain Rule/Unitary Method PDFQ1) 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. |