Brain Teaser: Topsy-Turvy

Topsy-Turvy

Q. Mange Lal was often absentminded. One day he went to the bank to withdraw some money but forgot the exact amount he wanted to withdraw, with the result that he inter-changed rupees and paise he required.

On his way back home he made some purchases: mangoes for Rs. 10.40; 1 kg soap for Rs. 7; two toys worth Rs. 3 each were bought by him for Rs. 2 each. On reaching home he saw that the balance amount left with him after the above purchases was double the amount he wanted to withdraw.

Now, you are required to assess the amount Mange Lal had written on his cheque.

Answer

A. Mange Lal wanted to withdraw Rs. 38.99 from the bank by mistake he withdrew Rs. 99.38.

Note:

Since he withdrawn rupees in place of paise and vice-versa, both the amounts cannot exceed figure 99.
Suppose the withdrawn amount is Rs. A and Paise B, then, 100A+B-2140=2 x (100B +A). In other words; 98A – 199B=2140-(1).
In order to arrive at the second equation we have to take into account 40 paise that he had spent.
This gives the following equation:

B-40=2A=B-40
100+B-40=2 A or 2A=B+60.
200+B-40=2A or 2A=B+160.
Now, out of the above three equations only one would agree with the first obtained equation 98A-199B=2140, which determines the value of ‘A’ & ‘B’.

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Topsy-Turvy