The allotment officer is trying to come up with a method to calculate fair division of funds across
various affected families so that the fund amount and amount received per family can be easily
adjusted based on daily revised numbers. The total fund allotted for a village is x x6 20 9 x 3 2 + + + .
The officer has divided the fund equally among families of the village and each family receives an
amount of x x2 2 2 + + . After distribution, some amount is left.
(i) How many families are there in the village?
(a) x + 4 (b) x - 3
(c) x - 4 (d) x + 3
(ii) If an amount of <1911 is left after distribution, what is value of x ?
(a) 190 (b) 290
(c) 191 (d) 291
(iii) How much amount does each family receive?
(a) 24490 (b) 34860
(c) 22540 (d) 36865
(iv) What is the amount of fund allocated?
(a) Rs 72 72 759 (b) Rs 75 72 681
(c) Rs 69 72 846 (d) Rs 82 74 888
(v) How many families are there in the village?
(a) 191 (b) 98
(c) 187 (d) 195
Answers
Given : The total fund allotted is formulated by the officer is x³ + 6x² + 20x + 9
divided the fund equally among families of the village
each family receives an amount of x² + 2x + 2 and After distribution, an amount of 10x+ 1 is left
To Find : How many families are there in the village
an amount of ₹1911 is left after distribution, what is value of x
Solution :
x + 4
x² + 2x + 2 _| x³ + 6x² + 20x + 9 |_
x³ + 2x² + 2x
___________
4x² + 18x + 9
4x² + 8x + 8
________________
10x + 1
x + 4 families are there in the village
10x + 1 = 1911
=> 10x = 1910
=> x = 191
amount each family receive x² + 2x + 2
= 191² + 2(191) + 2
= 36865
amount of fund allocated = x³ + 6x² + 20x + 9
191³ + 6(191²) + 20(191)+ 9
= 71,90,586
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