1.

Fill up the missing digit. If (128)a = (450)b then (16)a = (  )10

Answer»

L.H.S. contains 2 & 8, so a 2 and a ≠ 8. 

R.H.S. contains 4 and 5, so b ≠ 2. 

L.H.S. < R.H.S. so a > b and a ≠ b also.

The possible values of a and b are given below.

abReason
108 onlya>b and a ≠ b
168 or 10a>b and a ≠ b

Case I: 

a = 16 and b = 8 

(128)16 = (296)10 

(450)8 = (296)10 

So, a = 16 and b = 8. 

Then (16) = 1 × 16 + 6 × 160 = (22)10



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