# 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

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

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