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Shortcut 65:
Time, Work and Resource
\(\frac{W_1}{W_2}=\frac{R_1T_1}{R_2T_2} \)
Question:
If 10 men can cut 40 trees in 4 days, how many trees can be cut by 40 men 6 days?
Answer:
R1 = 10; R2 = 40
T1 = 4; T2 = 6
W1 = 40; W2 = ?
Substitute the values in the above formula, we get
40/W2 = (10 x 4)/(40 x 6)
W2 = 240 trees

Shortcut 66:
Work, Resource, Days and Hours
\(\frac{W_1}{W_2}=\frac{R_1T_1:H_1}{R_2T_2:H_2} \)
Question:
30 men working 6 hours day for 50 days can make 2000 toys. How many hours per day should 40 men work for 60 days to make 3000 toys?
Answer:
R1 = 30; R2 = 40, (Resources in each case)
T1 = 50; T2 = 60, (Days in each case)
W1 = 2000; W2 = 3000, (Work in each case)
H1 = 6; H2 = ?, (Hours per day in each case)
Substitute the values in the above formula, we get
2000/3000 = (30 x 50 x 6)/(40 x 60 x H2)
H2 = 5(5/8) hours
H2 = 5 hours 32 minutes 30 seconds

Shortcut 67:
Two men working together
\(\frac{AB}{A+B} \)
Question:
A can complete a work in 40 days. B can complete the same work in 60 days. How long will they take to complete the work if they are working together?
Answer:
A = 40
B = 60
Substitute the values in the above formula, we get
Time taken together = (40 x 60)/(40 + 60)
= 24 days