The scores of Amal and Bimal in an examination are in the ratio

Question

The scores of Amal and Bimal in an examination are in the ratio 11 : 14. After an appeal, their scores increase by the same amount and their new scores are in the ratio 47 : 56. The ratio of Bimal’s new score to that of his original score is

A 3 : 2
B 4 : 3
C 5 : 4
D 8 : 5
E 5:8

A 3 : 2
B 4 : 3
C 5 : 4
D 8 : 5
E 5:8

Eternal · Answer

Let scores increased by x.
=>  \frac{(11 + x)}{(14 + x)}  = 47:56

=>  \frac{(11 + x)}{(14 + x)}  =  \frac{47}{56}

=> 616 + 56x = 658 + 47x

=> 9x = 42

=> x =  \frac{42}{9}

=> x=  \frac{14}{3}

The ratio of Bimal's new score to old score is (14 +  \frac{14}{3} ) / 14 =  \frac{4}{3}

Hence Answer is (B)

yasminguedes · Answer

Do you know if there is another way to solve this problem? If we do all this math, we never end below 2min;

Eternal · Answer

IMO simplifying the above equation is fairly easy

Let scores increased by x.

=>  \frac{(11 + x)}{(14 + x)}  =  \frac{47}{56}

=> 11*56 + 56x = 14*47 + 47x

=> 9x = 14*(47-44)  taking 14 as common

=> x=  \frac{14}{3}   cancelling out 3 from both sides and simplifying directly

The ratio of Bimal's new score to old score is (14 +  \frac{14}{3} ) / 14 =  \frac{4}{3}

vaibhav1221 · Answer

I open up 15-20 tabs with random DS and PS questions from this forum to do a mini quiz. This question was towards the end of that little quiz I was giving and I was short on time so I used a totally different approach. I could really use some help with the validity of this approach.

original ratio 11:14; gap = 3
new ratio 47:56; gap = 9

increased by 3x

Bimal's ratio 14->56 increased 4x

Possible ratios 3:4 or 4:3, because Bimal's score increased, it should be 4:3. Therefore, I pressed on B.

Now, was that a mere fluke and the approach is all hogwash or is that a thing that I don't know about? Or do I hail from a parallel universe and don't know about it yet.

Thanks in advance!

ScottTargetTestPrep · Answer

Let 11x and 14x be the original scores of Amal and Bimal and n be the increase in their scores. We can create the equation:

(11x + n)/(14x + n) = 47/56

56(11x + n) = 47(14x + n)

616x + 56n = 658x + 47n

9n = 42x

3n = 14x

At this point, we see that n can be 14 and x can be 3. If that is the case, the Bimal’s original score is 14(3) = 42 and his new score is 42 + 14 = 56. Therefore, the ratio of Bimal’s new score to that of his original score is 56/42 = 8/6 = 4/3.

Answer: B

yamaza · Answer

yes, my answer may be too late but it may help anyone else in the future

old ration 11:14 (11-14 = 3)
new 47:56 (47-56=9)

we need to make the difference between the both same , because when same number is added to new and old no then difference between should be same

so lcm of 3 and 9 is 9
 
 11:14 *3 = 11*3:14*3
 47:56*1 = 47:56

the required ration is 56:14*3 ie  4:3

Kinshook · Answer

Given: The scores of Amal and Bimal in an examination are in the ratio 11 : 14. After an appeal, their scores increase by the same amount and their new scores are in the ratio 47 : 56.

Asked: The ratio of Bimal’s new score to that of his original score is

The scores of Amal and Bimal in an examination are in the ratio 11 : 14. 
Let us assume that the scores of Amal and Bimal in an examination are 11x & 14x respectively

After an appeal, their scores increase by the same amount and their new scores are in the ratio 47 : 56. 
(11x + y): (14x + y) = 47: 56
56(11x + y) = 47(14x + y)
616x + 56y = 658x + 47y
9y = 42x
3y = 14x

The ratio of Bimal’s new score to that of his original score   = (14x + y) : 14x = (3y + y):3y = 4:3

IMO B

Evronredor · Answer

A way around to avoid the calculation,

Old ratio -  A:B =11x:14x (where x is an unknown multiplier)
Difference = 3x

New ratio -  A:B = 47y:56y
Difference = 9y

We know when the same number is added to two different numbers, the difference between those two numbers will remain the same.

3x=9y => x=3y

The required ratio is Bimal’s new score to that of his original score,
56y:14x
Substituting x=3y
56y:14(3y) => 56y: 42y => 4:3 which is our answer option B

bumpbot · Answer

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The scores of Amal and Bimal in an examination are in the ratio

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