# Aptitude - Ratio and Proportion - Discussion

Discussion Forum : Ratio and Proportion - General Questions (Q.No. 4)

4.

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?

Answer: Option

Explanation:

Originally, let the number of seats for Mathematics, Physics and Biology be 5*x*, 7*x* and 8*x* respectively.

Number of increased seats are (140% of 5*x*), (150% of 7*x*) and (175% of 8*x*).

140 | x 5x |
, | 150 | x 7x |
and | 175 | x 8x |
|||||||

100 | 100 | 100 |

7x, |
21x |
and 14x. |

2 |

The required ratio = 7x : |
21x |
: 14x |

2 |

14*x* : 21*x* : 28*x*

2 : 3 : 4.

Discussion:

74 comments Page 1 of 8.
Abhishek Bansal said:
5 years ago

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.

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.

Subho said:
4 years ago

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.

So, new seats ratio are 7:10.5:14.

= 2:3:4.

Neelam said:
1 decade ago

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.

Himesh said:
4 years ago

@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?

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?

Insaan said:
2 years ago

@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.

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.

Vedanth said:
7 years ago

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.

5x + 40% of 5x.

= 7x.

7x + 50%of 7x

=10.5x.

8x + 75% of 8x

=14x.

So,

= 7x : 10.5x : 14x.

= 2 : 3 : 4.

Amrutha said:
5 years ago

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.

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.

(1)

Faizan said:
9 years ago

Previous ratio is 5:7:8, now by adding increase.

we get,

5+0.4*5 : 7+0.5*7 : 8+0.75*8 , which is 7:10.5:14.

Now it is simplified as 70:105:140 (by multiplying 10 with all).

And on simplifying by 7, we get new ratio as 2:3:4 .

we get,

5+0.4*5 : 7+0.5*7 : 8+0.75*8 , which is 7:10.5:14.

Now it is simplified as 70:105:140 (by multiplying 10 with all).

And on simplifying by 7, we get new ratio as 2:3:4 .

Mahesh said:
5 years ago

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?

Can anyone solve this?

Saif said:
7 years ago

@Aparna it is correct and the right way to solve this problem.

After this, you compare the ratio.

7/20 : 21/40 : 7/10.

Now bring the denominator to 40.

14/40 : 21/40 : 28/40.

14 : 21 : 28.

Simplify by 7.

2 : 3 : 4.

After this, you compare the ratio.

7/20 : 21/40 : 7/10.

Now bring the denominator to 40.

14/40 : 21/40 : 28/40.

14 : 21 : 28.

Simplify by 7.

2 : 3 : 4.

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