A sum of 2400 to be distributed among 6 top
participants of a contest. If each prize amount is 40 less than
its preceding amount, find the highest prize amount
Answers
The highest prize money is 500 Rs
Given:
A sum of 2400 to be distributed among 6 top participants of a contest
If each prize amount is 40 less than its preceding amount
To find:
Find the highest prize amount
Solution:
Given that each prize money is 40 less than the preceding amount
Let x be the highest amount and 1st price
Then the 2nd prize must 40 less than x
and third prize must be 40 less than 2nd prize
In this pattern the 6 prizes amounts will be as shown below
x, x - 40, x - 2(40), x- 3(40), x - 4(40), x - 5(40)
As we know sum of all these are equals to 2400
⇒ x+ x - 40 + x - 2(40) + x- 3(40) + x - 4(40) + x - 5(40) = 2400
⇒ 6x - 40 - 80 - 120 - 160 - 200 = 2400
⇒ 6x - 600 = 2400
⇒ 6x = 3000
⇒ x = 500
Therefore, the highest prize money x = 500 Rs
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Answer: The amount of highest prize is 500.
Step-by-step explanation:
According to the question,
Value of the given 6 prizes are in A.P.
Sum of all prizes (S) = 2400
common diffrence (d) = -40
Number of prizes(n) = 6
on applying A.P. formula of sum
⇒S=
⇒
⇒
divide the equation by 6
⇒
transfer 100 from other side
⇒
⇒
The highest prize amount is 500rs.
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