Q12 of 37 Page 195

To dig a well of x dcm deep. One part of the total expenses varies directly with x and other part varies directly with x2. If the expenses of digging wells of 100 dcm and 200 dcm depths are ₹ 5000 and ₹ 12000 respectively, let us write by calculating the expenses of digging a well of 250 dcm depth.

Given:

Acc. To given condition:


First part of expense (t1) ∝ x


Where x is the depth of well.


t1 = kx


second part of expense (t2) ∝ x2


t2 = mx2


total expense (t) = t1 + t2


It can be written as:


t = k x + m x2


First depth = 100 dcm and first expense = Rs.5000


5000 = k 100 + m(100)2)


5000 = 100k + 10000m …(1)


First depth = 200 dcm and first expense = Rs.12000


12000 = k 200 + m(200)2)


12000 = 200k + 40000m …(2)


Multiply (1) by 2 :


10000 = 200k + 20000m …..(3)


Subtract (3) from (2)


2000 = 20000m



Put m in (1)



5000 = 100k + 1000


100k = 5000 – 1000


100k = 4000


⇒ k = 40



For x = 250 dcm




⇒ t = 10000 + 6250


t = Rs16250


So total expene will be Rs. 16250


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