Question
The average of first two numbers and last two numbers of
a set of six numbers is 70 and 45 respectively. If the overall average of all six numbers is 65, find the average of third and fourth number.Solution
Let the six numbers be a, b, c, d, e, f. a + b = 2 
 70 = 140 ....................... (i) e + f = 2  45 = 90 ........................ (ii) a+ b + c + d + e + f = 6  65 = 390 ........................(iii) We get the sum of third and fourth digit by subtracting (i) and (ii) from (iii) a+ b+ c + d + e + f – a – b – e - f = 390 – 140 – 90 =160 ∴ c + d = 160  ∴ Required average =   = 80
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