a sum of ruppes 3750 is to be used to give ten cash prize to the students of a school for their overall academic performance. if each prize is rupee 50 less than the preceding prize, find the value of each prize.
Answers
Let the first student be given Rs x.
Then x + (x - 50) + (x - 100) + (x - 150) + (x - 200) + (x - 250) + (x - 300) + (x - 350) + (x - 400) + (x - 450) = 3750
=> 10x - 50 - 100 - 150 - 200 - 250 - 300 - 350 - 400 - 450 = 3750
=> 10x - 2250 = 3750
=> 10x = 3750 + 2250
=> 10x = 6000
=> x = 600
Therefore,
x - 50 = 600 - 50 = 550
x - 100 = 600 - 100 = 500
x - 150 = 600 - 150 = 450
x - 200 = 600 - 200 = 400
x - 250 = 600 - 250 = 350
x - 300 = 600 - 300 = 300
x - 350 = 600 - 350 = 250
x - 300 = 600 - 400 = 200
x - 350 = 600 - 450 = 150
Therefore, the values of each prize are 600, 550, 500, 450, 400, 350, 300, 250, 200 and 150.
Let the value of the prices be
x,x−50,x-100, .....
This is an arithmetic sequence with first term (a)=xand common difference (d)=−50.
Given,
Sn = 3750
d=-50
n=10
Using the formula:
Sn= n/2[2a + (n - 1)d]
3750=5(2a+9×-50)
750+450=2a
a=600
hence the first term of the AP is 600
first student will get rupees 600
2nd student will get rupees 550
third student will get rupees 500
fourth student will get rupees 450
fifth student will get rupees 400
sixth student will get rupees 350
seventh student will get rupees 300
8th student will get rupees 250
ninth student will get rupees 200
10th student will get rupees 150