Rs. 280 is to be distributed among four prize | vedclass

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(A) Let the four prizes be in an Arithmetic Progression $(AP)$.Let the first prize be $a$.Since each successive prize reduces by $Rs. 20$,the common d

Vedclass · Accepted Answer

$100, 80, 60, 40$

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(A) Let the four prizes be in an Arithmetic Progression $(AP)$.Let the first prize be $a$.Since each successive prize reduces by $Rs. 20$,the common difference $d = -20$.The number of prizes $n = 4$.The sum of the prizes $S_n = 280$.The formula for the sum of $n$ terms of an $AP$ is $S_n = \frac{n}{2} [2a + (n - 1)d]$.Substituting the values: $280 = \frac{4}{2} [2a + (4 - 1)(-20)]$.$280 = 2 [2a + 3(-20)]$.$140 = 2a - 60$.$2a = 200$,so $a = 100$.The four prizes are $a, a+d, a+2d, a+3d$.Substituting $a = 100$ and $d = -20$: $100, 100-20, 100-40, 100-60$.Thus,the prize amounts are $Rs. 100, Rs. 80, Rs. 60, Rs. 40$.

$Rs. 280$ is to be distributed among four prizes. If the prize amount in each successive prize reduces by $Rs. 20$,find the amounts paid in those prizes.

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