The table represents the total number of students studying courses P, Q, R, S and T across eight institutes, i. e. a, B, C, D, E, F, G and H.

Courses	Institutes
	A	B	C	D	E	F	G	H
P	520	410	550	450	570	210	750	450
Q	410	540	610	580	380	550	570	310
R	430	210	390	530	730	510	530	480
S	350	280	570	320	410	480	610	460
T	370	480	380	250	180	370	590	660

What is the ratio of the total number of students studying in Institute A to the total number of students studying in Institute H?

Correct option is A

​$$\textbf{1. The total number of students in Institute A:} \\[5pt]\text{Total} = 520 + 410 + 430 + 350 + 370 = 2080 \\[10pt]\textbf{2. Calculate the total number of students in Institute H:} \\[5pt]\text{Total} = 450 + 310 + 480 + 460 + 660 = 2360 \\[10pt]\textbf{3. Find the ratio of students in Institute A to Institute H:} \\[5pt]\text{Ratio} = \frac{\text{Students in Institute A}}{\text{Students in Institute H}} \\= \frac{2080}{2360} \\[10pt]\textbf{4. Simplify the ratio:} \\[5pt]\text{Greatest Common Divisor of 2080 and 2360 is 40} \\[5pt]\frac{2080}{40} = 52 \quad \text{and} \quad \frac{2360}{40} = 59 \\[5pt]\text{Therefore, the simplified ratio is } 52:59$$​​