Math, asked by bboy1837, 9 months ago

Puzzle time -- A man sent his servant to the bank to encash a cheque with amount Rs AB.XY paise written on it . The cashier gave the servant Rs XY . AB paise by mistake . The servant dropped 17 paise on the way and gave back remaining amount to the master. The money was twice the amount written on the cheque . So what amount was written on the cheque ?

Answers

Answered by amitnrw
0

Given : A man sent his servant to the bank to encash a cheque with amount Rs AB.XY paise written on it . The cashier gave the servant Rs XY . AB paise by mistake  

To find :  what amount was written on the cheque

Solution:

Amount of Cheque = AB.XY

Value = 10A + B  Rs  & 10X + Y Paise

Amount received  = XY.AB

Value = 10X +Y  Rs  &   10A  + B Paise

10X +Y Rs   + 10A + B - 17  Paise = 2 ( 10A + B  Rs  & 10X + Y Paise)

The money was twice the amount written on the cheque

=> Either  10X + Y = 2(10A + B)        or 10X + Y  = 2(10A + B) + 1

Case 1 : 10X + Y = 2(10A + B)  

2(10A + B)  Rs +  10A + B - 17  Paise  = 20A + 2B Rs + 2( 2(10A + B)  )

=>  10A + B - 17  Paise   =  2( 2(10A + B)  )

=> 3(10A + B) = -17  not possible

Case 2 : 10X + Y = 2(10A + B)  + 1

2(10A + B )+ 1    Rs +  10A + B - 17  Paise  = 20A + 2B Rs + 2( 2(10A + B )+ 1  )

=> 1 Rs  +  10A + B - 17  Paise   =  40A + 4B + 2   Paise

=> 81 Paise =  30A + 3B

=> 27 Paise = 10A + B

10A + B = 27

A = 2  ,   B = 7

10X + Y  = 2(27) + 1  = 55

X = 5  , Y = 5

Amount written on the cheque = 27.55  Rs

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