Nptel Assignment Question

Question

if 93 /4 = 23, the base of the number system is 

1. 8
2. 9
3. 10
4. 11

Answer 1

Let’s suppose the base is b.Convert both of them to base 10 then do algebric simplification.

As 9 is digit so b must be more than 9.Directly you can eliminate option a and b.

93 in base b is = (3+9*b) in base 10. similarly, 32 in base b is = (3+2*b) in base 10. 4 is same for both as b>9.

(3+9*b)/4=(3+2*b) → 3+9*b=12+8*b → b=9 But b should be more than 9.

Answer 2

The answer must be option d.

Reason: As in the question digit 9 is present so the base of the number system must be greater than 9.So eliminate option a and b.

Option c cannot be true as if the number system is of base 10 then the value of LHS should be (93/4)=23.25 which is not equal to the RHS.

So option d must be correct.

Answer 3

Base cannot be 9 or 8 because largest digit in given question is 9 then base must be >9. Hence, option a and b is eliminated.

Now check for option c, if base 10, 93/4=23.25 but in question 93/4=23 is given, this option is also eliminated.

Now only one option is left, Lets check for Base 11,

9x11¹+3x11⁰= 99+3=102 (in decimal), 4x11⁰=4 (in decimal), 2x11¹+3x11⁰=25 (in decimal).   102/4=25.5  which is equal to 23.555….(base11).​​​​ which is also not equal to 23. This option is also eliminated.  Hence no option is correct

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Comments

in case of option d, you're rounding... but why not option C ?

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actually ques is poorly formatted.. sorry i have done silly mistake previously, now i have edited… none is answer