Question

7. A shopkeeper had a weighing balance with uneven
pans. The left and the right pans of the balance
weighed 0.6 kg and 0.95 kg respectively. When the
shopkeeper placed some rice in the left pan and
standard weights in the right pan until the pans
leveled, he had to use 'ab'kg (where 'ab' is a two-digit
number) of the standard weights. If instead, he placed
the rice in the right pan and standard weights in the
left pan until the pans leveled, he had to use (ba'
+18.7) kg of the standard weights. The actual weight
of rice placed in the pans can be?​

Answer 1

Given :   A shopkeeper had a weighing balance with uneven  pans. The left and the right pans of the balance  weighed 0.6 kg and 0.95 kg respectively.

To find: the actual weight  of rice placed in the pans can be

Solution:

Let say Actual Weight of Rice = R  kg

The left   pan weighs = 0,.6 kg

right pans weighs = 0.95 kg

Weight in Left Pan = R + 0.6  kg

Weight in Right Pan  =   ab  + 0.95  kg

=>  R + 0.6 = ab  + 0.95

right pans weighs = 0.95 kg

Weight in Right Pan = R + 0.95  

Weight in Left Pan = ba + 18.7 + 0.6  kg

=> R + 0.95    =  ba + 18.7 + 0.6

=> 0.35 = ba + 18.7 - ab  - 0.35

=> ab  - ba = 18

=> 10a + b -  10b -  a  = 18

=> 9a - 9b = 18

=> a - b  = 2

R =  ab + 0.35  kg

R =  ba  + 18.35  kg

Hence actual Weight will end  with  0.35 kg

a - b  = 2

Possible Weight Can be

31.35 kg

42.35  kg

53.35  kg

64.35 kg

75.35 kg

86.35 kg

97.35  kg

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