**Shortcut 65:**

Time, Work and Resource

*[latex]\frac{W_1}{W_2}=\frac{R_1T_1}{R_2T_2} [/latex]*

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

*[latex]\frac{W_1}{W_2}=\frac{R_1T_1:H_1}{R_2T_2:H_2} [/latex]*

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

*[latex]\frac{AB}{A+B} [/latex]*

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