X paid ₹ 47 for certain cups of tea and coffee. If tea costs ₹ 5 per c

X paid ₹ 47 for certain cups of tea and coffee. If tea costs ₹ 5 per cup and coffee costs ₹ 8 per cup, which one of the following statements is correct ?

He drank 8 cups of tea and coffee.
He drank the same number of cups of tea and coffee.
He drank more tea than coffee.
He drank more coffee than tea.
This question was previously asked in
UPSC CISF-AC-EXE – 2017
He drank more coffee than tea.
Let ‘t’ be the number of cups of tea and ‘c’ be the number of cups of coffee. The cost equation is 5t + 8c = 47. We need to find non-negative integer solutions for t and c.
We can try possible values for c:
If c=0, 5t = 47 (not possible for integer t)
If c=1, 5t = 47 – 8 = 39 (not possible for integer t)
If c=2, 5t = 47 – 16 = 31 (not possible for integer t)
If c=3, 5t = 47 – 24 = 23 (not possible for integer t)
If c=4, 5t = 47 – 32 = 15 => t = 3. This is a valid integer solution (t=3, c=4).
If c=5, 5t = 47 – 40 = 7 (not possible for integer t)
If c=6, 5t = 47 – 48 = -1 (not possible for non-negative t)
The only valid solution is t=3 cups of tea and c=4 cups of coffee.
Based on this solution:
A) Total cups = 3 + 4 = 7, not 8. (Incorrect)
B) Number of tea cups (3) is not the same as coffee cups (4). (Incorrect)
C) He drank 3 cups of tea and 4 cups of coffee. 3 is not more than 4. (Incorrect)
D) He drank 4 cups of coffee and 3 cups of tea. 4 is more than 3. (Correct)
This is a simple linear Diophantine equation where we are looking for non-negative integer solutions. Since the coefficients are relatively small, trial and error is an efficient method to find the solution.