Aptitude - Ratio and Proportion - Discussion

We are given --> M : P : B = 5:7:8 . Increased in seats by 40% , 50% & 75%.
So this we can write as M:P:B = 5x : 7x: 8x (assuming common multiplier be x)
for simplicity of answering i am assuming x as 10.
So Before Increase Math seats = 5*10 = 50.
Similarly , Physics = 70 & Biology = 80.

Now Comes the increasing part.
Math by 40 % = 50*40/100 = 20.
So New Seats for math = (Earlier Available + New Seats) (50 + 20) = 70 Seats.
Similarly For physics it will be by 50 % = 70 * 50/100 = 35 & New Seats = 70+35 = 105.

For Biology New seats would be = 140.
After calculation, New Seats Are 70 : 105 : 140.
Simplify It & Answer would be 2:3:4.

Very good explanation, Thanks.

Seats for maths, science and arts in a school are in the ratio 5:7:8.there is a proposal to increase these seats by x%, y%, z% respectively. And the ratio of increased seats is 2:3:4. Find x, y, z.

Can anyone solve this?

Will the percent increase not be 40/100 into 5x + 5x and so on?

As this is increased percentage?

The required ratio = 7x : 21x/2: 14x

14x : 21x : 28x where did the 2 of 21/2 go?
2 : 3 : 4.

Anyone, Please explain for me.

Very good explanation, Thanks @Harjinder Singh.

If it's decreasing to 40% then what is the answer?

Thanks for the answer @Harjinder.

7 : 8 = 50 : 70 : 80 then
40% :50% :75% = 70 : 105 : 140.

So, 14 : 21 : 28 = 2 : 3 : 4 is the answer.