How many vadapavs per day are made with cheese and tomato as fillings?

Question

These questions are based on the following data. At Goli - Vadapav—a famous fast food centre in Andheri in Mumbai, vadapavs are made only on an automatic vadapav making machine. The machine continuously makes different sorts of vadapavs by adding different sorts of fillings on a common bread. The machine makes the vadapavs at the rate of 1 vadapav per half a minute. The various fillings are added to the vadapavs in the following manner. The 1st, 3^rd, 5th, 7th,…vadapavs are filled with a chicken patty; the 1^st , 5^th , 9th, …..vadapavs with vegetable patty; the 1st, 8th, 15th, 22th, …..vadapavs with mushroom patty; and the rest with plain cheese and tomato fillings. The machine makes exactly 500 vadapavs per day.

  How many vadapavs per day are made with cheese and tomato as fillings?

Answer 1

Total vadapavs made = 500 

Vadapavs with chicken and mushroom patty =250 (Number of terms in the series 1,3, 5, 7, 9...499) out of which half of the vadapavs also have vegetable petty.

Vadapavs with only mushroom patty = 36 (Number of terms of the series 8, 22, 36, ….)

Vadapavs with chicken, mushroom and vegetable patty = 18 (Number of terms in the series 1, 29, 57... 

Required answer = 500 − 250 – 36 = 214.