Question

The ratio of the number of students studying Arts to that studying commerce in Institute E is. (Total Arts = 3800, Total Commerce = 4200)

• A. 19:16
• B. 19:27
• C. 19:28
• D. 27:14

Hint:

To find the ratio of quantities from different pie charts, you can also set up the ratio using the percentages and totals directly: \( (%_1 \times \text{Total}_1) : (%_2 \times \text{Total}_2) \).
Ratio = \( (14 \times 3800) : (18 \times 4200) = (14 \times 38) : (18 \times 42) \).
Simplify this ratio by canceling common factors before multiplying to save time.

Answer 1

The Correct Option is B

We need to find the number of students in Institute E for both streams and then find their ratio.
Arts Students from Institute E:
From the Arts pie chart, the percentage for Institute E is 14%. Total Arts students = 3800.
Number of Arts students in E = 14% of 3800 = \( \frac{14}{100} \times 3800 = 14 \times 38 = 532 \).
Commerce Students from Institute E:
From the Commerce pie chart, the percentage for Institute E is 18%. Total Commerce students = 4200.
Number of Commerce students in E = 18% of 4200 = \( \frac{18}{100} \times 4200 = 18 \times 42 = 756 \).
Ratio: Ratio (Arts : Commerce) = 532 : 756. Now we simplify the ratio by finding the greatest common divisor. Both numbers are divisible by 4.
\( 532 \div 4 = 133 \) \( 756 \div 4 = 189 \) The ratio is 133 : 189. Both numbers are divisible by 7.
\( 133 \div 7 = 19 \) \( 189 \div 7 = 27 \) The simplified ratio is 19 : 27.