# Shortcut of Time and work-1

Shortcut 62:
Time taken is directly proportional to work.
$\frac{W_1}{W_2}=\frac{T_1}{T_2}$
Question:
It took 40 days to build 10 buildings. How long will it take to build 50 buildings using same number of employees?
W1 = 10; W2 = 50
T1 = 40; T2 = ?
Substitute the values in the above formula, we get
10/50 = 40/T2
T2 = 200 days

Shortcut 63:
Time taken is inversely proportional to resources
$\frac{R_1}{R_2}=\frac{T_2}{T_1}$
Question:
If 20 men can do the work in 40 days, how many men are required to do the same work in 10 days?
R1 = 20; R2 = ?
T1 = 40; T2 = 10
Substitute the values in the above formula, we get
20/R2 = 10/40
R2 = 80

Shortcut 64:
Resources are directly proportional to work
$\frac{R_1}{R_2}=\frac{W_1}{W_2}$
Question:
40 men are required to complete 20 buildings. How many men are required to build 50 buildings in the same time?
R1 = 40; R2 = ?
W1 = 20; W2 = 50
Substitute the values in the above formula, we get
40/R2 = 20/50
R2 = 100

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