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.

5 it is increased by 40% = 5 * 40/100 = 2.
7 it is increased by 50% = 7 * 50/100 = 7/2.
8 it is increased by 75% = 8 * 75/100 = 6.
We need to add the ratios with their increased values.
(5) +2 : (7) +7/2 : (6) + 8.
7 : 21/2 : 14.

Multiply 2 on all sides.
14: 21: 28.
Divide 7 on all sides.
2: 3 : 4.

Math seats 5 increased will be 4% = now number of total seats 7. Physics seats 7 increased will be 50% = now number of total seats = 10.5. Bio seats 8 increased will be 75%= now the total number of state 14.

So, new seats ratio are 7:10.5:14.
= 2:3:4.

As 5:7:8 totals to 20 so can we assume value say 2000 and can make proportion of value in the given ratio,and then can increase the value by the given percentage of 40,50 and 75,by doing this i m getting increased ratio as 2:3.5:6 can u please make me understand by this method.

@All.

Would this formula be applicable if the number of seats is to be DECREASED rather than INCREASED?

And the ratios themselves are decreasing after solutions, how then the seats were increased? could anyone tell me why the ratios decreased instead of increasing?

5 : 7 : 8
Let it be,
500:700:800
Maths increased by 40%, 40%of 500 = 200,
Physics increased by 50%, 50%of 700 = 350,
Biology increased by 75%, 75%of 800 = 600.
Therefore;
500 + 200 = 700.
700 + 350 = 1050.
800 + 600 = 1400.

700 : 1050 : 1400 simplified as 2 : 3 : 4.

@Ram Kundu.

7x : 21x/2 : 14x from 14x : 21x : 28
To make the same denominator we have to multiply with 2 (7x*2/2 and 14*2/2)

14x/2 : 21x/2 : 28x/2 ( now we have the same denominator) we can ignore the denominator
Take LCM of 14x: 21x: 28x,
We get 2x: 3x: 8x.

Let the seats be 5x, 7x, 8x they are increasing by 40%, 50%, 75%.
5x + 40% of 5x.
= 7x.

7x + 50%of 7x
=10.5x.

8x + 75% of 8x
=14x.
So,
= 7x : 10.5x : 14x.
= 2 : 3 : 4.

@All.

Here 5:7:8 is not the original no of seats.

So, Initially, we assume the no of seats as 100% for each. so each is increased to 140%, 150%, and 175% respectively.

To know how many seats are required we are multiplying 140% * 5.

For make calculation easy take the values as 500 : 700 : 800,

40% of 500 =200,
50% of 700 =350,
75% of 800=600,
Then the increased ratio = 700 :1050:1400.

After simplification, the answer would be 2:3:4.