Aptitude - Ratio and Proportion - Discussion

Discussion :: 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?

[A]. 2 : 3 : 4
[B]. 6 : 7 : 8
[C]. 6 : 8 : 9
[D]. None of these

Answer: Option A

Explanation:

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

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

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

14x : 21x : 28x

2 : 3 : 4.


Shwetha said: (Nov 11, 2010)  
Why is the %age value changing from 40 to 140, 50 to 150 and 75 to 175 ?

Can anyone explain in detail please?

Malli said: (Nov 20, 2010)  
Because initial amount is 100 then 100+40=140 etc.

Praveen said: (Dec 2, 2010)  
Any shortcut for this ?

Richa said: (Dec 3, 2010)  
@ shwetha

when it is said that there is x% or y% increase in any value then to find out that increased value we have do
100+x

as in this example a value increased 40% means 100+40=140

Ramesh said: (Dec 9, 2010)  
5:7:8 = 50:70:80
50*140/100=70 ; 70*150/100=105 ; 80*175/100=140
70: 105: 140 or
14: 21: 28 or
2: 3: 4

Hari said: (Jan 23, 2011)  
Good shortcut ramesh.

Vivek Mishra said: (Apr 15, 2011)  
Thanks to giving a good salution with shortcut.

Sandi said: (Apr 22, 2011)  
Very good shortcut ramesh.

Mariah said: (Apr 28, 2011)  
Can we apply this shortcut for other problems?

Harjinder Singh said: (Jun 18, 2011)  
1. 40% of 5 = 2, total seats 5+2=7
2. 50% of 7 = 7/2 total seats 7+7/2=21/2
3. 75% of 8 = 6 total seats 8+6=14
now compare ratios of all 7:21/2:14=>14:21:28
=>2:3:4

Sunita said: (Jul 6, 2011)  
Very good and easy method singh. Keep it up.

Emani Karthik Reddy said: (Jul 23, 2011)  
Thanks singh for easy to solve the problems.Keep it up.

Priyabrata said: (Sep 26, 2011)  
Thanks Harjinder, Very easy method apply you.

Kushi said: (Oct 14, 2011)  
Thanks harjinder.

Gnaneswar said: (Jan 3, 2012)  
Singh concept is correct.

Satish said: (Feb 10, 2012)  
Hi guys cool,

5:7:8

5*1.4 : 7*1.5 : 8*1.75

7 : 10.5 : 14

2 : 3 :4

Important NOTE : KEEP in fractions instead of decimals.

Rahul Singh said: (Mar 14, 2012)  
Let their Ratio be 5X,7X,8X. INCRISED %=140%,150%,175%
ATQ , 5X OF 140=7X,150%OF 7X=21/2X,175%OF 8X=12.

Their Ratio = 7X:21/2X:14X.

Taking LCM of Denominator, we get = 14:21:28=2:3:4

Neelam said: (Apr 28, 2012)  
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.

Sonal Mahajan said: (Jun 7, 2012)  
Hi ramesh

Can you tell me please how it comes?
70: 105: 140 or
14: 21: 28 or
2: 3: 4

Rupali said: (Jun 20, 2012)  
HI sonal! ramesh divided 70,105,140 by 5 then answer will be 14:21:28 after that by 7 therefore answer is 2: 3: 4

Bharadwaj said: (Aug 21, 2012)  
Ramesh and Harjinder was explained well :).

Nikhil said: (Apr 16, 2013)  
@Harjinder can you please tell me how do we find out?

1. 40% of 5 = 2, total seats 5+2 = 7.

2. 50% of 7 = 7/2 total seats 7+7/2 = 21/2.

3. 75% of 8 = 6 total seats 8+6 = 14.

Bala said: (Jan 3, 2014)  
Why we should add 100+x?

Mk.Raj said: (Mar 18, 2014)  
Because% mean 100, than 40% increase means 140.

Sarika said: (Mar 29, 2014)  
Ratio is 5:7:8.
Increase in % i.e 140, 150 and 175.

Then, 5*140 = 700.
7*150 = 1050.
8*175 = 1400.

Ratio = 700:1050:1400.
70:105:140.

Answer = 2:3:4.

Faizan said: (Jul 1, 2014)  
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 .

Aaanikt said: (Jul 21, 2014)  
5/2 = 2.5(approx 2).
7/2 = 3.5(approx 3).
8/2 = 4.

Than ratio is 2:3:4.

Ramesh said: (Aug 12, 2014)  
Say the ratio is 5:7:8. What is their denominator and how it has come. And if it is 20 then wouldn't it be like this 15x/20x = 140/100 and 7x/20x= 150/100. Does 15/20 indicates 100 percent here.

Barun Nag said: (Dec 5, 2014)  
How 14x:21x:28x becomes 2:3:4?

Ganesh said: (Jan 25, 2015)  
Hey @Barun.

14/7, 21/7, 28/7.

Aparna said: (Jul 16, 2015)  
5x/20+5/20*40/100 = 7x/20.

7x/20+7x/20*50/100 = 21x/40.

8x/20+8x/20+75/100 = 7x/10.

Can any one help me is it correct if yes what are the next steps please help me to understand.

Babita Yadav said: (Oct 11, 2015)  
40% of 5 = 140/100*5 = 7.

50% of 7 = 150/100*7 = 21/2.

75% of 8 = 175/100*8 = 14.

Now take common 7.

7 (14:21:28) = 2:3:4.

J K Reddy said: (Feb 21, 2016)  
I have small doubt any sum I can do this modal?

Biradar said: (Apr 4, 2016)  
Thanks to all it helps me a lot.

Rubesh said: (Jun 14, 2016)  
40% of 5 = 140/100 * 5 = 7.
50% of 7 = 150/100 * 7 = 21/2.
75% of 8 = 175/100 * 8 = 14.

Now take common 7.

7(14 : 21 : 28) = 2 : 3 : 4.

Saif said: (Jul 26, 2016)  
@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.

Saisangeetha said: (Aug 3, 2016)  
@Ramesh.

Very good explanation.

Ajit Raj said: (Aug 5, 2016)  
Mindblowing explanation, Thank you all.

Vedanth said: (Aug 31, 2016)  
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.

Shikha said: (Sep 7, 2016)  
Thanks @Ramesh.

Maji Ali said: (Nov 3, 2016)  
What is 20% of 50% of 75% of 70? Please tell me the answer.

Sikander said: (Jan 7, 2017)  
Isn't that simple like if we add 40% + 50% + 70% = 165,
40/165 = 2.
50/165 = 3.
75/165 = 4.

Isaactamson said: (Feb 26, 2017)  
The 40% of 5 =2,
50% of 7=3.5,
75% of 8 = 6,

The ratio will be 2:3:6.

Isaactamson said: (Feb 26, 2017)  
The 40% of 5 =2,
50% of 7 = 3.5,
75% of 8 = 6,
(5+2)x2 = 14,
(7+3.5)x2 = 21,
(8+6)x2 = 28,
= 16:21:28.

The ratio will be 2:3:4.

Priya said: (Jul 29, 2017)  
Very good explanation, Thanks @Harjinder Singh.

Priya said: (Jul 29, 2017)  
Sikander can you explain in what aspect you are taking?

Pankaj said: (Sep 13, 2017)  
Very good explanation, Thanks.

Sivaji said: (Sep 13, 2017)  
Increase % means 100+x% so 140, 150, 175values are add to 50, 70, 80 then ratio are 2:3:4.

Raju said: (Sep 16, 2017)  
Anyone, Please explain for me.

Zee said: (Oct 2, 2017)  
The required ratio = 7x : 21x/2: 14x

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

Ishit Setia said: (Dec 30, 2017)  
Will the percent increase not be 40/100 into 5x + 5x and so on?

As this is increased percentage?

Abhishek Bansal said: (Feb 11, 2018)  
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.

Amrutha said: (Feb 18, 2018)  
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.

Ahmad said: (Mar 19, 2018)  
Awesome, thanks @Ramesh.

Mahesh said: (Aug 18, 2018)  
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?

Afsal said: (Sep 16, 2018)  
If it's decreasing to 40% then what is the answer?

Sujith said: (Nov 11, 2018)  
Thanks for the answer @Harjinder.

Mukesh said: (Jan 6, 2019)  
7 : 8 = 50 : 70 : 80 then
40% :50% :75% = 70 : 105 : 140.

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

Dipendra said: (Jul 4, 2019)  
Only increased seats?

How is it possible? Please tell me.

Himesh said: (Sep 3, 2019)  
@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?

Subho said: (Sep 9, 2019)  
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.

Himanshu said: (Nov 13, 2019)  
5:7:8 means 5/20 which means 0.25.

2:3:4 means 2/9 which means 0.22.

But it is saying that the seats have increased. But according to maths the seats have decreased.

Can anyone please tell me how is this possible?

Rahul said: (Nov 19, 2019)  
Let the ratio 500:700:800.
Increase 200:350:600.
700:105:1400=14:21:28=2:3:4 answer.

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