The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero ?

In a game of 1000 meters, If A scores 1000 meters then B scores 950 meters and C scores 920 meters.
? B runs 1000 m while C scores 920 x 1000 / 950= 18400 / 19 m
Hence, in 1000 m race, B can give C (1000 - 18400 / 19) = 600 / 19 = 31¹¹?₁₉ meters start.

? log_a3 = 1/3
? 3 = (a)^1/3
? a = 27

Let the number be N,
Then, 137.5% of N = 33
? N = (33 x 100)/137.5 = 24

SP = 100/12 paise
Let's CP = x
SP = 0.8x = 100/12
? x = 10/(0.8x12) paise
Therefore, CP = 100/9.6 paise

Thus the new SP (with 20% profit) = 100/9.6 X 1.2 = 100/8 paise
Hence, 8 apples can be purchased for Rs.1 to gain 20%

CP = (100/30) x 400 = ? 4000/3
[? CP = {100/(100 - Loss%)} x SP]

Cost of the horse paid by A = (4860 x 100) / 81 = Rs. 6000
Cost of the horse paid by C = (6000 x 117) / 100 = Rs. 7020
Gain of B = Rs. 7020 - Rs. 4860 = Rs. 2160