Question 133

Six numbers are arranged in decreasing order. The average of the first five numbers is 30 and the average of the last five numbers is 25. The differences of the first and the last numbers is:

Solution

Let the numbers (in decreasing order) be $$a,b,c,d,e,f$$

Average of first 5 = 30

=> Sum of first 5 numbers = $$30\times5$$

=> $$(a+b+c+d+e)=150$$ --------------(i)

Similarly, sum of last 5 = $$25\times5$$

=> $$(b+c+d+e+f)=125$$ --------------(ii)

Subtracting equation (ii) from equation (i),

=> $$a-f=150-125=25$$

Thus, the differences of the first and the last numbers = 25

=> Ans - (C)

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