Question

24 men complete a work in 16 days and 32 women complete it in 24 days. 16 men and 8 women started that work and worked for 12 days in the remaining work is to be completed in 4 days, the number of men to be further added to the existing workforce is

1. 16
2. 14
3. 12
4. 9

Answer 1

Correct Answer - Option 1 : 16

Given:

24 men complete a work in 16 days.

32 women complete work in 24 days.

Formula Used:.

M1.D1.T1.E1W1.C1=M2.D2.T2.E2W2. M1.D1.T1.E1W1.C1=M2.D2.T2.E2W2. Where,

\(\frac{{M1.D1.T1.E1}}{{W1.C1}} = \;\frac{{M2.D2.T2.E2}}{{W2.C2}}\)

M is the number of working men

D is the total number of days

T is total hours of working days

E is the efficiency of working men

W is total work

C is the consumption of working men

Calculation:

Now by using the formula,

24 men × 16 = 32 women × 24

⇒ m = 2w

m = 2 and w = 1      ---- (efficiency)

Total work,

24 men × 16

⇒ 24 × 2 × 16

⇒ 768 units

Now 16 men and 8 women worked for 12 days,

⇒ {16(2) + 8(1)} × 12

⇒ 40 × 12

⇒ 480 units completed by them.

Remaining work,

⇒ 768 – 480

⇒ 288 units 

This unit needs to be completed in 4 days,

Now using the formula,

Let the working men be x

{x(2) + 8(1)} × 4 = 288

⇒ (2x + 8) = 72

⇒ 2x = 64

⇒ x = 32

32 men required to complete the remaining work in 4 days.

The increased number of men are 32 – 16 = 16

∴ The number of men required more is 16.