Work it out

It’s quite strange that sometimes there are situations where what you have been studying and practicing comes face to face with what actually occurs in day to day life.
For instance, the mathematical/aptitude problems is something all of us have done at some point or the other in our lives. But sometimes, you tend to create such problems on your own.

Just try and figure this one out if you can.

I go to my office daily via the DND flyway, where I have to pay Rs. 11 as toll for each trip. I have got a member card for that, which I get recharged for 50 trips every time I see the low balance warning on the screen, which displays the balance when you tap the card. But due to the sun or may be out of hurry, I am not able to see the balance every time on the screen. The only thing worrying is when the balance is not a multiple of 11.

And your worst dreams do come true when the inflation rate is so high. So one day when I tapped my card, against the machine, it didn’t show up a multiple of 11 as balance. A few days later I got to know that the rates had gone up by a rupee. After some days of the revised rates, I got my card recharged again for 50 trips. Yesterday, my card balance read Rs. 625.

What I need to figure out is : –

1. Since how many trips have I been paying more toll on the flyway?

2. What was my card balance when I last tapped my card with the older rates?

Can anyone help me out with this? Please mention how you got to the answer as well.

Thanks.

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2 Comments

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  1. There would be multiple possible solutions to this problem.

    1. After 3, 15, 27 or 39 days.
    2. Should be easy to calculate after you know the answer to 1.

    The way to calculate this is to convert your problem into an analytical puzzle with various variables and constants. The main variables to be calculated are 2 (1. No of days you paid the old price 2. No of days you paid the new price). Since there are multiple combinations for the two variables with the sum as 50, just run a small program or manually balance out the equation with the combinations.

  2. I agree! There are multiple solutions to this problem.

    I did it this way!
    Out of the early Rs.550 (supposing that you got it recharged when you had zero balance) with which you got your card recharged, some part got deducted according to the Rs 11 toll charges, say “m” and some by the Rs 12 charges, say “n”.

    So, the equation which we can frame is :

    550 – 11m – 12n = 25
    or
    525 = 11 (m+n) + n

    Solving this, we get :

    1. 8,19,30,41 as the possible number of trips

    2. 121, 253, 385, 517 as the possible balance when you last tapped your card with the older rates.

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