The analysis of recently held CBSE exam shows that Chennai Zone, Delhi Zone and Ajmer Zone have performed the best. The average marks of the Ajmer Zone & Delhi Zone put together is 71%. The average marks of Chennai Zone & Delhi Zone put together is 76% and the average marks of Chennai Zone & Ajmer Zone put together is 79%. What is the range of the average marks of all the three zones ( N ) put together. a) 71%<N<78% b) 70.5%<N<77.5% c) 73.5%<N<77.5% d) 73%<N<79%

Average of Ajmer = A; number of students in Ajmer = a Average of Delhi = D; number of students in Delhi = d Average of Chennai = C; number of students in Chennai = c (aA+dD)/(a+d) = 71;(cC+dD)/(c+d) = 76;(cC+aA)/(c+a) = 79; Cross-multiplying and adding the equations, 2Aa + 2Dd + 2Cc = 150a + 147d + 155c Because a, d and c are independent, equate the like terms So, 2A = 150 => A = 75; 2C = 155 => C = 77.5; 2D = 147 => D = 73.5 So, the maximum and minimum values of (aA+dD+cC)/(a+d+c) are 77.5 and 73.5 respectively 73.5 < N < 77.5