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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$100, 80, 60, 40$

Vedclass · Answer

(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.

Similar Questions

The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \frac{3n^{2}}{2} + \frac{5n}{2}$. Find the $25^{th}$ term of the $A.P.$

Determine $k$ so that $k^{2}+4k+8, 2k^{2}+3k+6, 3k^{2}+4k+4$ are three consecutive terms of an $AP$.

With respect to the usual notations of an $A.P.$,if $T_{n} = 4$,$d = 2$,and $S_{n} = -14$,find $n$ and $a$.

Which term of the $A.P.$ $5 \frac{1}{2}, 11, 16 \frac{1}{2}, \ldots$ is $550$ (in $^{th}$)?

If $2x$,$x+10$,and $3x+2$ are three consecutive terms of an $A.P.$,find the value of $x$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module