In the first M games of a team's season, the ratio of the

Question

In the first M games of a team's season, the ratio of the team's wins to its losses was 1:2. In the subsequent N games, the ratio of the team´s wins to losses was 1:3. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?

A. 7:18
B. 9:23
C. 11:27
D. 23:54
E. 31:77

A. 7:18
B. 9:23
C. 11:27
D. 23:54
E. 31:77

arpanpatnaik · Accepted Answer

The choice , I feel should be 31:77. **Request you to look into the source for the value. As for the solution, if M is the games played in the first half, Total wins = M/3 Total Losses = 2*M/3 Similarly for N games, with the ratio 1:3 Total wins = N/4 Total Losses = 3N/4 Hence when combined, total games become M+N Total wins = M/3 + N/4 Total losses = 2M/3 + 3N/4 Now with the above, we know M:N = 4:5 i.e. M = 4N/5. Substituting the values, Total wins = 31N/60 Total losses = 77N/60 Hence the ratio is 31:77. Please correct me if I am wrong!

Regards, Arpan

mau5 · Answer

As the final ratio is being asked, we can consider the value of M:N as 48:60.
 
First M(48) games, Wins = 16;Losses = 32

Succesive N(60) games, Wins = 15;Losses = 45

Total Wins:Total Losses = (16+15)/(32+45) = 31/77
E.

imhimanshu · Answer

Are you sure that the option E is 37:77. I'm getting 31:77.

josemarioamaya · Answer

I corrected the answer choice e it is 31:77

avinashrao9 · Answer

Why cant we consider 12:15 and end up with the ratio 9:23 which is option (B)

mau5 · Answer

You will never got 9:23 for 12:15 .You will still get 31:77.

avinashrao9 · Answer

I considered the ratio wrong.. Though 12:15 satisfies 4:5 condition, it does not work out for the number of matches mentioned. It has to be 48:60.. Thanks :-D

pkhats · Answer

How about 12:20, its a perfect fit for 4:5 - M:N, an also all the other ratios.. and with this result I get 9:23.. really confused why this is the wrong answer..

Any help from the experts will be of great help!

Bunuel · Answer

4:5 = 8:10 = 12: 15  =  16 :20 = ... but not 12:20.

mittalg · Answer

12:20 is  3:5  and not 4:5 as required. 
We know that the ratio of in first M games in 1:2 which means, we have denominator as 3 if we want to find the numbers of wins and losses.
In second case, the ratio of next N games is 1:3, making denominator 4.

Now M = 4x = 4 * 12x = 48 x (We are choosing 12 as it is LCM of 3 & 4)
 N = 5x = 5* 12x = 60 x
Hence, we are taking the ratio as 48:60 and not any other ratio. Hope it helps!!!

pkhats · Answer

Oh!

Thanks both, Silly me! 
These silly mistakes are gonna make me cry one day - Hope not! :p

Donnie84 · Answer

M = 4/9 of total games
N = 5/9 of total games

Wins out of M games = 1/3
Losses out of M games = 2/3

Wins out of N games = 1/4
Losses out of N games = 3/4

At this point, we should look at the denominators and come up with the least common multiple.
LCM (9,3,4) = 108. This gives us the total number of games.

M = (4/9)*108 = 48
N = (5/9)*108 = 60

Wins out of M games = (1/3)*48 = 16
Losses out of M games = (2/3)*48 = 32

Wins out of N games = (1/4)*60 = 15
Losses out of N games = (3/4)*60 = 45

Total wins = 16 + 15 = 31
Total losses = 32 + 45 = 77

Desired ratio = 31/77

Answer (E).

CAMANISHPARMAR · Answer

\frac{Total Wins}{Total Losses}  =  \frac{(16+15)}{(32+45)} = \frac{31}{77}

Option E is the correct answer

gracie · Answer

let M=3x
let N=4y
3x/4y=4/5→
x/y=16/15
3*16=M=48 games: 16 wins; 32 losses
4*15=N=60 games: 15 wins; 45 losses
(16+15)/(32+45)=31/77
E

JeffTargetTestPrep · Answer

Using the given ratio M:N of 4:5, we can let M = 4(12) = 48 and N = 5(12) = 60. So in the first 48 games, the team has ⅓(48) = 16 wins and ⅔(48) = 32 losses, and in the subsequent 60 games, the team has ¼(60) = 15 wins and ¾(60) = 45 losses. So the team’s win-loss ratio is (16 + 15)/(32 + 45) = 31/77.

Answer: E

gvij2017 · Answer

Understood the explanation using magic numbers, but here I am confused when I used balance method.

Look! 
for m games- W/L= 1/2 
for n games- W/L= 1/3 
for m+n games = W/L = x
m:n= 4/5

from balance method 
(1/3 -x)/(x-1/2) = m:n = 4/5 
here I got x= 11/27.

now please tell me where I am wrong.

Rupesh1Nonly · Answer

M/N = 4/5 Or we could say 48/60

In M matches(48) : 16 won and 32 lost
In N matches (60): 15 won and 45 lost

In M+N: (16+15)won and (32+45) lost

which gives 31/77

hope it helps

sayiurway · Answer

I have the same concern. Could any expert explain how to use the balance method here?
Thank you.

Sahil20o7 · Answer

hey this question can be solved very easily.

ratio of m:n = 4:5 
i.e if 4x + 5x games were played total would have been = 9x 
hence the total number of games played is a multiple of 9
check for the options where the sum of wins and losses is also a multiple of 9.

or

you could start assuming the number of games played m:n as 4:5 or 8:10 or 20:25 or 48:60 so on and when the number of games played i.e both in m and n which should be equal to the total wins + total losses .
this might take few tries

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