Question

In a University examination, six students, Sachin, Ashish, Tanwi, Ankit, Ramesh and Suresh had written the following three papers, Economics, Finance and Accounts. The examination comprised of two parts, internals and externals. The table below shows the performance of each of these six students in this examination.

Part A: Indicates the total marks scored by the student in that paper as a percentage of the total marks of all the six students put together in that subject.

Part B: Indicates the marks scored by that student in internals as a percentage of total marks scored by that student in that subject.

From the table below it can be inferred that Sachin had obtained 30% of marks in Economics out of the total marks obtained by all the six students in Economics put together. Whereas out of the marks scored by him in Economics, the marks scored by him in Internals accounted for 20% of marks.
$\begin{array}{ccccccc}& Economics& & Finance& & Accounts& \\ & PartA& PartB& PartA& PartB& PartA& PartB\\ Sachin& 30& 20& 25& 10& 25& 10\\ Ashish& 10& 35& 10& 0& 20& 5\\ Tanwi& 15& 25& 10& 10& 10& 0\\ Ankit& 10& 30& 5& 10& 10& 10\\ Ramesh& 20& 40& 20& 10& 30& 25\\ Suresh& 15& 15& 30& 5& 5& 10\end{array}$

If the ratio of marks obtained by Ankit in the internals of all three subjects (Economics, Finance and Accounts) in that order is 9:3: 4, then what was the ratio of marks scored by Sachin in the externals of those three subjects in the same order?

• A. 18 : 10 : 5
• B. 3 : 1 : 2
• C. 17 : 51 : 67
• D. 24 : 45 : 30

Answer 1

The correct option is D 24 : 45 : 30

Let the total marks scored by the six students in Economics, Finance and Accounts be x, y and z respectively.
$\therefore$ The ratio of marks scored by Ankit in the Internals of these papers would be:
$\left(30\%of10\%ofx\right):\left(10\%of5\%ofy\right):\left(10\%of10\%ofz\right)$ which would be the same as (0.03x) : (0.005y) : (0.01z) = (3x) : (0.5y) : (z)
But, (3x) : (0.5y) : (z) is equal to 9 : 3 : 4.
$\therefore$ 3x = 9, 0.5y = 3 and z = 4
$\therefore$ The ratio x: y: z would be equal to 3:6: 4.
The marks scored by Sachin are $30\%,25\%and25\%$, the ratio of marks would be 90:150: 100, i.e. 9:15: 10.
Now, the marks scored by Sachin in Internals are $20\%,10\%and10\%$.
$\therefore$ Marks scored by him in Externals will be $80\%,90\%and90\%$.
$\therefore$ The required ratio would be $\left(80\%of9\right):\left(90\%of15\right):\left(90\%of10\right)$, i.e. (7.2) : (13.5) : (9)
This ratio would be equal to 72 : 135 : 90 or 24 : 45 : 30.