Question

*CHALLENGE FOR MATHEMATICIANS*

Here is a mathematical quiz to solve.
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A man gave a cheque to his servant and asked to get it encashed from bank. Cheque was for few rupees and paisas ( Rs.ab.xy).

बैंक कै्शियर ने गलती से चैक में जितने रुपए थे, उतने पैसे और जितने पैसे थे, उसकी जगह उतने रुपए नौकर को दे दिए। (Means, cashier gave give Rs. xy.ab. in place of Rs. ab.xy).

On the way to home, नौकर ने उसी पैसों मे से 20 पैसे की बीङी पी ली। और बाकी सारे पैसे मालिक को लाकर दे दिए।



Now question is *WHAT WAS THE AMOUNT

Answer 1

Let us take the number of rupee is x and that of paise is y

Then written on cheque = 100x + y paise

Amount given by cashier = 100y + x paise

Servant spent = 20 paise

Amount left = 100y + x - 20 paise

By the given conditions,

100y + x - 20 = 2 (100x + y)

or, 100y + x - 20 = 200x + 2y

or, 199x = 98y - 20

or, x = (98y - 20)/199

We need to find a 2 digit integral value of x and 2 digit integral value of y.

Let us put y = 10, 11, 12, 13, ... and calculate the value of x.

When y = 10, x = 4.824...

When y = 11, x = 5.317...

When y = 12, x = 5.809...

..... ..... ..... .....

..... ..... ..... .....

When y = 53, x = 26.

Here both x = 26 and y = 53 are integral values in two digits.

So it was written Rs. 26.53 on cheque.

Confirmation:

• Written >> Rs. 26.53
• Cash given to servant >> Rs. 53.26
• Spent by servant >> Rs. 0.20
• Cash given to the man >> Rs. 53.06
• Rs. 53.06 = 2 * Rs. 26.53

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