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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 after increased seats?
- a)2 : 3 : 4
- b)6 : 7 : 8
- c)6 : 8 : 9
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Seats for Mathematics, Physics and Biology in a school are in the rati...
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number after increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
⇒ (140 / 100 x 5x), (150 / 100 x 7x) and (175 / 100 x 8x)
⇒ 7x, 21x / 2 and 14x.
⇒ 7x, 21x / 2 and 14x.
∴ the required ratio
= 7x : 21x / 2 : 14x
⇒ 14x : 21x : 28x
⇒ 2 : 3 : 4.
⇒ 14x : 21x : 28x
⇒ 2 : 3 : 4.
Most Upvoted Answer
Seats for Mathematics, Physics and Biology in a school are in the rati...
Let's assume initial seats for maths, physics and biology be 5x, 7x and 8x respectively
after increase:
maths: 5x + 40% of 5x = 5x + 2x =7x
physics: 7x + 50% of 7x = 7x + 3.5x = 10.5x
biology: 8x + 75% of 8x = 8x + 6x = 14x.
simplify by dividing each tern by 0.5x
New ratio is: 14:21:28 = 2:3:4
so answer is 2:3:4
after increase:
maths: 5x + 40% of 5x = 5x + 2x =7x
physics: 7x + 50% of 7x = 7x + 3.5x = 10.5x
biology: 8x + 75% of 8x = 8x + 6x = 14x.
simplify by dividing each tern by 0.5x
New ratio is: 14:21:28 = 2:3:4
so answer is 2:3:4
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Community Answer
Seats for Mathematics, Physics and Biology in a school are in the rati...
Ratio of seats before increase: 5 : 7 : 8
Let's increase the seats as per the given proposal:
- Mathematics seats increased by 40%: 5 + (40/100) * 5 = 7
- Physics seats increased by 50%: 7 + (50/100) * 7 = 10.5 ≈ 11
- Biology seats increased by 75%: 8 + (75/100) * 8 = 14
New ratio of seats: 7 : 11 : 14
Now, we need to simplify this ratio. We can do this by dividing all the numbers by the smallest number in the ratio, which is 7.
- 7 : 11 : 14 (divide by 7)
- 1 : 1.57 : 2 (approximate to nearest whole numbers)
- 1 : 2 : 2
Therefore, the ratio of seats after the increase is 1 : 2 : 2, which is equivalent to 2 : 3 : 4 (multiply all numbers by 2).
Hence, the correct answer is option A) 2 : 3 : 4.
Let's increase the seats as per the given proposal:
- Mathematics seats increased by 40%: 5 + (40/100) * 5 = 7
- Physics seats increased by 50%: 7 + (50/100) * 7 = 10.5 ≈ 11
- Biology seats increased by 75%: 8 + (75/100) * 8 = 14
New ratio of seats: 7 : 11 : 14
Now, we need to simplify this ratio. We can do this by dividing all the numbers by the smallest number in the ratio, which is 7.
- 7 : 11 : 14 (divide by 7)
- 1 : 1.57 : 2 (approximate to nearest whole numbers)
- 1 : 2 : 2
Therefore, the ratio of seats after the increase is 1 : 2 : 2, which is equivalent to 2 : 3 : 4 (multiply all numbers by 2).
Hence, the correct answer is option A) 2 : 3 : 4.
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