### Brain Teasers

# Nastee's Workers

In the early years of the last century, a MADADIAN industrialist, Nastee, had employed 100 labourers to build his new improved Kebab and Rat Poison factory. Things were a little different those days, and the employment of labourers' wives and children was commonplace, although Nastee did not allow any woman to work without her husband. Also, at least half the men working came with their wives.

He paid five Madadian Wonks per day to each man, four Wonks to each woman and one Wonk to each child. He gave out 200 Wonks every evening.

How many men, women and children were working with Nastee?

He paid five Madadian Wonks per day to each man, four Wonks to each woman and one Wonk to each child. He gave out 200 Wonks every evening.

How many men, women and children were working with Nastee?

### Answer

16 men, 12 women and 72 children were working with Nastee.Let's assume that there were X men, Y women and Z children working with Nastee Hence,

X + Y + Z = 100

5X + 4Y + Z = 200

Eliminating X and Y in turn from these equations, we get

X = 3Z - 200

Y = 300 - 4Z

If a woman works, her husband also works, and at least half the men working came with their wives; the value of Y lies between X and X/2. Substituting these limiting values in equations, we get

if Y = X,

300 - 4Z = 3Z - 200

7Z = 500

Z = 500/7 i.e. 71.428

if Y = X/2,

300 - 4Z = (3Z - 200)/2

600 - 8Z = 3Z - 200

11Z = 800

Z = 800/11 i.e. 72.727

But Z must be an integer, hence Z=72. Also, X=16 and Y=12

There were 16 men, 12 women and 72 children working with Nastee.

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