Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50%, and 75% respectively. What will be the ratio of increased seats?
Question
Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50%, and 75% respectively. What will be the ratio of increased seats?
Solution 1
The current ratio of seats for Mathematics, Physics, and Biology is 5:7:8.
Step 1: Calculate the increase in seats for each subject.
For Mathematics, an increase of 40% means the new ratio will be 5 + (40/100)*5 = 7.
For Physics, an increase of 50% means the new ratio will be 7 + (50/100)*7 = 10.5.
For Biology, an increase of 75% means the new ratio will be 8 + (75/100)*8 = 14.
Step 2: Simplify the ratio.
The new ratio of seats for Mathematics, Physics, and Biology is 7:10.5:14.
To simplify this, we can multiply each number by 2 to get rid of the decimal in Physics.
This gives us a final ratio of 14:21:28.
Solution 2
The current ratio of seats for Mathematics, Physics, and Biology is 5:7:8.
Step 1: Calculate the increased seats for each subject.
For Mathematics, the increase is 40% of 5. So, the increase is 0.40 * 5 = 2 seats. The total seats for Mathematics after the increase will be 5 + 2 = 7 seats.
For Physics, the increase is 50% of 7. So, the increase is 0.50 * 7 = 3.5 seats. The total seats for Physics after the increase will be 7 + 3.5 = 10.5 seats.
For Biology, the increase is 75% of 8. So, the increase is 0.75 * 8 = 6 seats. The total seats for Biology after the increase will be 8 + 6 = 14 seats.
Step 2: Find the new ratio.
The new ratio of seats for Mathematics, Physics, and Biology will be 7:10.5:14.
However, to simplify this ratio, we can multiply each number by 2 to get rid of the decimal.
So, the simplified ratio will be 14:21:28.
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