Question

There are 8 kids – A, B, C, D, E, F, G and H. Two hundred one rupee coins are to be distributed among them in such a way that the distribution forms an arithmetic progression. Find the total number of coins received by C and F ?

• A. 24
• B. 36
• C. 48
• D. 50
• E. 64

Answer 1

The Correct Option is D

To solve the problem of distributing 200 one-rupee coins among 8 kids such that the distribution forms an arithmetic progression (AP), we proceed as follows:

1. Label the number of coins received by the 8 kids as \(a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8\).
2. In an arithmetic progression, each term can be expressed in terms of the first term \(a\) and the common difference \(d\). Thus:
   • \(a_1 = a\)
   • \(a_2 = a + d\)
   • \(a_3 = a + 2d\)
   • \(a_4 = a + 3d\)
   • \(a_5 = a + 4d\)
   • \(a_6 = a + 5d\)
   • \(a_7 = a + 6d\)
   • \(a_8 = a + 7d\)
3. The total number of coins is given by the sum of these terms: a_1 + a_2 + a_3 + \ldots + a_8 = 8a + 28d = 200
4. Simplifying, we have: 8a + 28d = 200
5. Dividing the entire equation by 4 gives: 2a + 7d = 50   (Equation 1)
6. To find the sum of coins received by C and F, we need \(a_3\) and \(a_6\):
   • From AP sequence:
     • \(a_3 = a + 2d\)
     • \(a_6 = a + 5d\)
   • Sum of coins for C and F: a_3 + a_6 = (a + 2d) + (a + 5d) = 2a + 7d
   • Using Equation 1: 2a + 7d = 50

Therefore, the total number of coins received by C and F is 50.