question_answer

Out of three numbers the average of the first and the second number is 52 more than the average of the second and the third number. What is the difference between the first and the third number?              

A)  54                               

B)  154                 

C)  52                   

D) 100

E) 104

Correct Answer: E

Solution :

Let the three numbers be a, b and c respectively. Now, \[\left( \frac{a+b}{2} \right)-\left( \frac{b+c}{2} \right)=52\] or, \[a+b-b-c=52\times 2=104\] \[\therefore a-c=104\] a+b+k+360= 1700 Or, a+b+k=1340            ?.... (i) Again, a + c + k + 420 = 1740 or, a+c+k=1320              ... (ii) b+c+k+220= 1600 or, b+c +k= 1380               .. (iii) a + b + c + k + 360 + 220 + 420 = 2500 or, a+ b + c + k = 2500 - 1000 = 1500 ... (iv) Solving (i), (ii), (iii) and (iv), we get k=1040             or, a= 120, b= 180, c == 160