Out of 400 houses, each valued at Rs. 20,000, on an average 4 houses get burnt every year resulting in a combined loss of Rs. 80,000. What should be the annual contribution of each house owner to make good this loss?
Answers
Concept:
Percentage of loss = ((cost price - selling price)/(cost price))*100
Percentage of profit = ((selling price - cost price)/(cost price))*100
Sum of n terms of an Arithmetic Progression is
Sn = n/2[2a + (n − 1) × d]
where d is common difference and a is first term of
Given:
Out of 400 houses, each valued at Rs. 20,000, on an average 4 houses get burnt every year resulting in a combined loss of Rs. 80,000.
Find:
Annual contribution of each house owner to make good this loss.
Solution:
Cost of each house = Rs. 20000
Yearly 4 houses are burnt.
⇒ It takes 100 years for all 400 houses to be completely burnt.
Total money spent by owner = 400*20000 = 8000000 rupees
So, the owner should be able to recover at least 80 lakh rupees from those houses in 100 years.
Assuming constant annual rent 'r' for each house over 100 years, we get,
Total money earnt in 100 years = r(400 + 396 + 392 + ... + 8 + 4)
(∵ first year we have 400 houses, next year we have 396 and so on)
⇒ r(400 + 396 + 392 + ... + 8 + 4) ≥ 8000000
⇒ r( (100/2)*(2*4 + (100 − 1) × 4) ) ≥ 8000000
⇒ r( 50*(8 + 396) ) ≥ 8000000
⇒ r( 20200 ) ≥ 8000000
⇒ r ≥ 80000/202
⇒ r ≥ 396.0396
∴ The yearly rent of each house should be more than 396.04 rupees for the owner make good for the loss.
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