Simultaneous Equation Solution - 1

QUESTION


Solution:
Total No. of fruits initially in the basket = 11

Avg. Cost per fruit in the basket after replacement = 19.27...

Logic:
Let the no. of pears be A and that of peaches be O.
Let the cost of an pear be x and that of an peach be y.

Total cost = Ax + Oy = 248 .... Given
Avg cost of fruit = (Ax + Oy)/(A + O) = 248/(A + O)

Adding an Pear the equation becomes : (248 + x)/(A + O + 1) = Avg. + 2
Adding an Peach the equation becomes : (248 + y)/(A + O + 1) = Avg. - 1

Subtracting the above equations : (x - y)/ (A + O + 1) = 3
i.e. x-y = 3 (A + O + 1)

Also after the replacement of 2 pears by peaches the avg cost per fruit:
(248 - 2x + 2y)/(A + O) = 16
(248 -2(3(A + O + 1)))/(A + O) = 16
(248 - 6 - 6(A + O))/(A + O) = 16
242/(A + O) = 16 + 6
Therefore, A + O = 242/22 = 11

i.e Number of fruits initially in the basket = 11.

Avg cost after an pear is replaced by peach:
(248 - x + y)/(A + O) = (248 - 36)/11 = 212/11 = 19.27....