Number of seats for Mathematics, Physics and Biology in Senior Secondary School Siwani 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?

Options

A. `1:2:3`
B. `2:3:4`
C. `3:4:5`
D. `4:5:6`

Answer

To solve the problem step by step, we need to follow these steps:

### Step 1: Define the initial number of seats
Let the initial number of seats for Mathematics, Physics, and Biology be represented as:
- Mathematics = 5x
- Physics = 7x
- Biology = 8x

### Step 2: Calculate the increased number of seats
Now, we will calculate the increased number of seats based on the given percentages:
- For Mathematics, the increase is 40%:
\[ \text{Increased seats for Mathematics} = 5x + (40\% \text{ of } 5x) = 5x + 0.4 \times 5x = 5x + 2x = 7x \]

- For Physics, the increase is 50%:
\[ \text{Increased seats for Physics} = 7x + (50\% \text{ of } 7x) = 7x + 0.5 \times 7x = 7x + 3.5x = 10.5x \]

- For Biology, the increase is 75%:
\[ \text{Increased seats for Biology} = 8x + (75\% \text{ of } 8x) = 8x + 0.75 \times 8x = 8x + 6x = 14x \]

### Step 3: Write the increased seats in ratio form
Now we have the increased seats as:
- Mathematics: 7x
- Physics: 10.5x
- Biology: 14x

The ratio of the increased seats is:
\[ \text{Ratio} = 7x : 10.5x : 14x \]

### Step 4: Simplify the ratio
To simplify the ratio, we can divide each term by x (since x is common) and also by 0.5 to eliminate the decimal:
\[ \text{Ratio} = 7 : 10.5 : 14 = 14 : 21 : 28 \]

Now, we can simplify this further by dividing each term by 7:
\[ \text{Ratio} = 2 : 3 : 4 \]

### Final Answer
The ratio of the increased seats for Mathematics, Physics, and Biology is:
\[ \text{Final Ratio} = 2 : 3 : 4 \]

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