A sum of Rs. 280 is to be used to award four prizes. If each prize after the first is Rs. 20 less than the next most valuable one, find the value of each of the prizes.

Solution

Since each prize is Rs. 20 less than its preceding prize, therefore, the values of the seven successive cash prizes will form an A .P.
Let the first prize be Rs. a. Then, Successive prize = Rs. (a – 20), Rs. (a – 40),
Rs. (a – 60)..........Here, first term = a
Common difference = (a – 20) – a = –20 n = 7 and S_n = 700
$We space know space that comma space space straight S subscript straight n equals straight n over 2 left square bracket 2 straight a plus left parenthesis straight n plus negative 1 right parenthesis straight d right square bracket rightwards double arrow space space space space space space space space space space space 700 equals 7 over 2 left square bracket 2 straight a plus left parenthesis 7 minus 1 right parenthesis left parenthesis negative 20 right parenthesis right square bracket rightwards double arrow space space space space space space space space space space 700 equals 7 over 2 left square bracket 2 straight a plus left parenthesis 6 right parenthesis left parenthesis negative 20 right parenthesis right square bracket rightwards double arrow space space space space space space space space space space 1400 space equals space 7 left square bracket 2 straight a minus 120 right square bracket rightwards double arrow space space space space space space space space space space space space 200 equals 2 straight a minus 120 rightwards double arrow space space space space space space space space space space space space space space 2 straight a equals 200 plus 120 rightwards double arrow space space space space space space space space space space space space space space space 2 straight a space equals 320 rightwards double arrow straight a space equals space 160$

Hence value of first prize = Rs. 160, and successive prizes are
Rs. (a – 20), Rs. (a – 40), Rs. (a – 60) ...
i.e. Rs. (160 – 20), Rs. (160 – 40), Rs. (160 – 60)...
i.e. Rs. 140, Rs. 120, Rs. 100 ...

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

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Arithmetic Progressions

A sum of Rs. 280 is to be used to award four prizes. If each prize after the first is Rs. 20 less than the next most valuable one, find the value of each of the prizes.

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

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For Daily Free Study Material Join wiredfaculty

Arithmetic Progressions

A sum of Rs. 280 is to be used to award four prizes. If each prize after the first is Rs. 20 less than the next most valuable one, find the value of each of the prizes.

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference– 5, – 1, 3, 7, . . .

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .