A student appeared in the Mock CAT. The test paper contained 3 sections namely QA, DI and VA. The percentage marks in all VA was equal to the average of percentage marks in all the 3 sections. Coincidentally, if we reverse the digit of the percentage marks of QA we get the percentage marks of DI. The percentage marks in VA scored by student could be:

A. 81

B. 48

C. 66

D. 69

E. None of these

Solution(By Examveda Team)

Let the percentage marks in QA =(10a + b)%
Let the percentage marks in DI = (10b + a)%
Let the percentage marks in VA = x%

Now, according to the question, we have,
\eqalign{ & \frac{{\left( {10{\text{a}} + {\text{b}}} \right) + {\text{x}} + \left( {10{\text{b}} + {\text{a}}} \right)}}{3} = {\text{x}} \cr & 11{\text{a}} + 11{\text{b}} + {\text{x}} = 3{\text{x}} \cr & {\text{or, x}} = \frac{{11\left( {{\text{a}} + {\text{b}}} \right)}}{2} \cr}
Clearly, we can see that the percentage of the VA section will be a multiple of 11
So, required answer will be 66
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