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Word Problem 5

Problem 5: If 4 men or 7 boys can do a work in 29 days, then 12 men and 8 boys will do the same work in;

a. 7 days          b. 8 days                     c. 9 days               d. 10 days

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Solution:

In such problems we pay our attention to the statement of the question. Here we note the words ‘or’ and ‘and’ in the statement!

or‘ means that 4 men are equal to 7 boys

i-e 4 M=7 B

=> 1 M = 7B/4

In the second part of the question ‘and‘ means — 12 men and 8 boys together !

i-e 12 M + 8 B

Put value of 1M in this  expression we get;

12 M + 8 B

= 12 ( 7B/4) + 8 B

= 3 x 7 B + 8 B

=21 B+ 8 B

=29 B

So, 12 men and 8 boys are equal to 20 boys !

Now we can talk only with reference to number of boys to get the solution of the problem – and  statement of the problem can be rephrased as;

“If  7 boys can do a work in 29 days, then 29  boys will do the same work in;

a. 7 days          b. 8 days                     c. 9 days               d. 10 days”

Keeping in view this revised statement we arrange data as under;

We put arrows in up and down directions because it is now a problem of inverse proportion i-e if there will be more boys to work, the work will finish in less number of days. So if one quantity (number of boys)  is increasing the other (number of days) is decreasing !

\Rightarrow \frac{x}{29}= \frac{7}{29}

\Rightarrow x= \frac{29\times7}{29}

\Rightarrow x=7

So, 12 men and 8 boys will finish the same work in 7 days !

 

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