Amitabh own a garden.In the garden, the number of mango trees is equal to number of mangoes per tree and the cost price per mango is the same as the number of mango trees in the garden. The maintenance cost is ₹ 860 per tree. If Amitabh sells one mango at ₹ 61, the overall loss in the business is ₹ 800. Find the number of mangoes in the garden, if no mangoes were wasted and the number of trees were more than 30.

Answer

N/a

Explanation

Let the number of mango trees int the garden=x
`:.` Number of mangoes per tree=x
`:.` Number of mangoes in the garden=`x^(2)` and cost price per mango=₹ x.
`:.` Total cost price of mangoes`= ₹ x^(3)`
Total maintenance cost= ₹ 860x
Total selling price`= ₹ 61x^(2)`
and loss in the business = ₹ 800
From the above information, we get
`x^(3)-61x^(2)+860x-800=0`.
On putting x=1, we have L.H.S.=0
`:. (x-1)` is a factor of `x^(3)-61x^(2)+860x-800` other factors can be obtained by long division method as follows:

`:. " " x^(3)-61x^(2)+860x-800=0`
`implies " "(x-1)(x^(2)-60x+800)=0`
`implies " "(x-1)(x-20)(x-40)=0`
`:. x=1 " "or x=20 " " or " "x=40`
But `" "x lt 30 " "`(given)
`:. " " x=40`
`:.` Total number of mangoes are `(40)^(2)` i.e., 1600. `" "` Ans.