Shortcuts for Chain Rules

Formula for Solving Chain Rule Easily

m_{1}\: d_{1}\: t_{1}\: s_{1}\: w_{2}\: a_{2}\: f_{2}=m_{2}\: d_{2}\: t_{2}\: s_{2}\: w_{1}\: a_{1}\: f_{1}

m - Men/labour

d - Days

t - Time

w - part of work done/ wages

a - Amount earned

f - Food consumed/Milk used/coal required Machines/Diesel required for pumps.

Chain Rules Examples


Question 1: A machine weaves 0.75 meter of cloth every second. Approximately, how many seconds will it take for the weave 20 meters of cloth?

Solution:

w_{1} = 0.75 m , w_{2} = 20 m

t_{1} = 1 s , t_{2} = ?

w_{2}\: t_{1}= w_{1}t_{2}

= t_{2}=\frac{w_{2}\: t_{1}}{w_{1}}=\frac{20\times 1}{0.75}=26.67 sec


Question 2: 30 men can complete a piece of work in 15 days. In how many days will 25 men complete the same work?

Solution:

m_{1} = 30 , m_{2} = 25

d_{1} = 15 days , d_{2} = ?

m_{1}\: d_{1}= d_{2}\: m_{2}

d_{2}=\frac{m_{1}\: d_{1}}{m_{2}}=\frac{30\times 15}{25}=\frac{450}{15} = 18 days


Question 3: 12 boys, working 3 hours a day can complete a work in 20 days. How many hours a day must 18 boys work to complete the same work in 10 days?

Solution:

b_{1} = 12 , b_{2} = 18

t_{1} = 3 Hrs , t_{2} = ?

d_{1} = 21 days , d_{2} = 10 days

b_{1}\: t_{1}\: w_{1}= b_{2}\: t_{2}\: w_{2}

t_{2}=\frac{b_{1}\: t_{1}\: w_{1}}{b_{2}w_{2}}=\frac{12\times 3\times 21}{18\times 10}=\frac{756}{180}=4Hrs(\approx )

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