Question

A SUM OF RS 1890 IS TO BE USED TO GIVEN SEVEN CASH PRIZES TO STUDENTS OF A SCHOOL IF EACH PRIZE IS RS 50 LESS THAN ITS PRECEDING PRIZE FIND VALUE OF EACH PRIZES

Answer 1

The problem is related to AP
Sum of 7 terms=1890
Common difference =d=-50
We know the formula
S(n) = n/2 × [2a+(n-1) d ]
S(7) = 7/2 × [2a+(7-1)*-50]
1890=7/2 × [2a+(6*-50)]
1890*2=7 × [2a-300]
3780=14a-2100
3780+2100=14a
5880=14a
a=5880/14
a=420
Hence required AP is
a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d
Since d is negative AP becomes
a, a-d, a-2d, a-3d, a-4d, a-5d, a-6d
Substituting a&d we get,
420, 420-50, 420-100, 420-150, 420-200, 420-250, 420-300
Hence prize money are
₹420, ₹370, ₹320, ₹270, ₹220, ₹170, ₹120
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