SOLUTION: please,sir,i request you to solve this question fast and urgently. the question is - an employer hired a man for seven weeks on the condition that if he worked for full seven week

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Question 85830: please,sir,i request you to solve this question fast and urgently.
the question is - an employer hired a man for seven weeks on the condition that if he worked for full seven weeks,he could get Rs 300 and a free holiday.but the man worked for 4 weeks and got Rs 30 and a free holiday.can you tell the value of this holiday?
Found 2 solutions by 303795, bucky:
Answer by 303795(562) About Me  (Show Source):
You can put this solution on YOUR website!
If he had worked the full time he would have earned an extra Rs 270 in 3 more weeks. He is therefore earning Rs 90 per week.
In four weeks he would earn 4 x 90 = Rs 360.
For that he received a holiday and Rs 30 so the holiday must be worth Rs 330.

Answer by bucky(2099) About Me  (Show Source):
You can put this solution on YOUR website!
For 7 weeks of work the man would get Rs 300 plus the holiday (call it H). This means that
each week the man earns one-seventh of Rs 300 + one-seventh of H. In equation form this is:
.
300%2F7+%2B+H%2F7
.
But the man only worked 4 weeks and he got Rs 30 + H. That means that each week he earned
one-fourth of what he got ... for each week of work he got:
.
30%2F4+%2B+H%2F4
.
Assuming that the weekly rates remained the same in both cases, you can set them equal and
the equation is:
.
30%2F4+%2B+H%2F4+=+300%2F7+%2B+H%2F7
.
Let's get rid of the denominators by multiplying both sides of this equation by a common
denominator of 28 (that is multiply all terms by 7 times 4) and the equation becomes:
.
%287%2A4%29%2A30%2F4+%2B+%287%2A4%29%2AH%2F4+=+%287%2A4%29%2A300%2F7+%2B+%287%2A4%29%2AH%2F7
.
Next cancel the terms in the denominators with the same terms in the numerators to reduce
the equation:.
.
%287%2Across%284%29%29%2A30%2Fcross%284%29+%2B+%287%2Across%284%29%29%2AH%2Fcross%284%29+=+%28cross%287%29%2A4%29%2A300%2Fcross%287%29+%2B+%28cross%287%29%2A4%29%2AH%2Fcross%287%29
.
and the equation becomes:
.
%287%2A30%29+%2B+7%2AH+=+%284%2A300%29+%2B+4%2AH
.
Multiply out the two "number" terms:
.
210+%2B+7H+=+1200+%2B+4H
.
Next, collect the terms containing H on one side of the equation and the numbers for Rs on the
other side. Begin by subtracting 4H from both sides of the equation:
.
210+%2B+7H+-+4H+=+1200+%2B+4H+-+4H
.
After the subtraction the equation is:
.
210+%2B+3H+=+1200
.
Next subtract Rs 210 from both sides of the equation:
.
210+-+210+%2B+3H+=+1200+-+210
.
After the subtraction the equation is reduced to:
.
+3H+=+990
.
Finally, solve for H (the value of the holiday) by dividing both sides of the equation
by 3 and you find that:
.
H+=+990%2F3+=+330
.
So the answer to the problem is that the Holiday, H, is worth Rs 330.
.
You can check this by calculating that in 4 weeks the man earned Rs 30 + H or Rs 30 + Rs 330
for a total of Rs 360. If you multiply this amount by the ratio 7%2F4 you find that
in 7 weeks he should earn:
.
%287%2F4%29%2A360+=+2520%2F4+=+630
.
Then you can compare this Rs 630 with the problem statement that says in 7 weeks he earns
Rs 300 + the holiday ... which is Rs 300 + Rs 330 ... a total of Rs 630. This is the same
answer we got by multiplying what he earned in 4 weeks by the ratio of 7%2F4 so the
answer of H = Rs 330 looks good.
.
Hope this helps you to understand the problem.