A shopkeeper mentally reversed the digits of a customer’s correct amou

Question

A shopkeeper mentally reversed the digits of a customer’s correct amount of change and thus gave the customer an incorrect amount of change. If his collection showed 54 cents more than it should have, which of the following could be the correct amount of change in cents?

(A) 24
(B) 35
(C) 64
(D) 75
(E) 93

(A) 24
(B) 35
(C) 64
(D) 75
(E) 93

GMATinsight · Answer

let, the change to be returned = ab
Chnges returned = ba

now, ab-ba = 54

i.e. (10a+b) - (10b+a) = 54

i.e. 9 (a-b) = 54

i.e. (a-b) = 6 i.e. difference of digits for correct answer should be 6 which is true for 93

Answer: Option E

MrCleantek · Answer

Can you please explain a bit more? Especially the last part

KarishmaB · Answer

Using Options:

If the shopkeeper had to give ab cents, he actually gave ba cents. At the end of the day, he had 54 cents extra. 
It means he had a give a higher amount ab (correct amount) but gave a smaller amount ba. 
So you tens digit should be greater than units digit and if you inverse the digits and subtract, you should get 54.
24, 35 - tens units less than units digit so outright rejected.
64 - 46 gives less than 20 - rejected
75 - 57 gives less than 20 - rejected
Answer 93 (93 - 39 = 54)

GMATinsight · Answer

MrCleantek 
Any Two digit number ab can be represented as 10a+b e.g. 57 = 10*5+7 and 73 = 10*7+3

Similarly, Any Three digit number abc can be represented as 100a+10b+c e.g. 257 = 100*2+10*5+7 and 473 = 100*4+10*7+3

I don't understand what problem are you facing at the end... Please highlight the part in which you need further explanation.

MrCleantek · Answer

I had confusion here: i.e. (a-b) = 6 i.e. difference of digits for correct answer should be 6 which is true for 93
But now I got it. I was using 54 and trying to come up with 93. I dont know what was I doing. Now I got it. 93 and 39 lead to 54 as diff. Diff between digits is also 6. So that is the answer

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A shopkeeper mentally reversed the digits of a customer’s correct amou

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

A shopkeeper mentally reversed the digits of a customer’s correct amou

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia