Word Problem 6

Work and Persons 0

Problem 6: If 3 men or 6 boys can do a work in 20 days, then 6 men and 8 boys shall take;

a. 6 days b. 8 days c. 10 days d. 7 days

— work and men –

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Solution:

3 men or 6 boys = 20 days

6 men and 8 boys = How many days ?

Data can be arranged as under:

Here note the words – ‘or’ & ‘and’ .

3 men or 6 boys means ;

$3 men = 6 boys$

or in short;

$3 m = 6 b$

$\Rightarrow m = 2 b$

i-e one man is equal to 2 boys !

While 6 men and 8 boys means;

6 man+ 8boys or in short , 6m+8b

But one man is equale to 2 boys i-e 1m = 2b, so putting value in above;

6m+8b = 6 (2b)+8b = 12b+8b=20b

i-e 6 men and 8 boys are equal to 20 boys

Now we rearrange data considering only boys and days;

This can be written as;

$\frac{?}{20}=\frac{6}{20}$

$\Rightarrow ?=\frac{6}{20} \times 20$

$\Rightarrow ?=6$

So, the answer to the question is 6 days i-e 6 men and 8 bys will take 6 days to finish the work

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