Latest TCS Aptitude Question SOLUTION: When numbers are written in base b, we have 15*22 = 414, the value of b is

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When numbers are written in base b, we have 15*22 = 414, the value of b is

Asked In TCS NIRAJ BARNWAL (10 years ago)

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Shashi Kumar Gupta  (10 years ago)

convert the given no. in decimal...
so..
(1*b^1+5*b^0)*(2*b^1+2*b^0)=(4*b^2+1*b^1+4*b^0)...

after solving above eq...
we get.. b = 6 so answer is 6

Is this solution Helpfull? Yes (21) | No   

babu rao ganpat rao apte  (10 years ago)

another way...
5*2=10... but we see denominator is 4.... so 10 must have been divided by 6 to give remainder 4 and a carry of 1..then next is 1*2=2 plus 1 from carry..thus it equals to 3. ..thus 15*22=34+X34...add them..answer is 414...thus base is 6...the main thing to feel is...whenever any calculation gets above 6...divide the number by six and write the remainder...it looks tough but once u will feel it...it will be the easiest method

Is this solution Helpfull? Yes (2) | No (1)  

Amit Kumar  (10 years ago)

(414)b => 4*b^2 + 1*b^1 + 4 = 15*22
now solve..

Is this solution Helpfull? Yes (1) | No (1)  

jhansirani  (10 years ago)

b=6.arthematic operations should be done in decimal number system.while converting this into decimal system we will get one quadratic equation by solving b is 6.

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Ankan Chakraborty  (8 years ago)

Multiply the last two digits of the LHS digits and equate to the last digit of RHS side
5*2=4
10=4
Ans base = 6

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aditya  (10 years ago)

6 z corrct

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Bharath Kumar  (9 years ago)

Let the base be b
15 in base b means the decimal value is b + 5
22 in base b means 2b+2
Similarly, 414 in base b is 4b^2 + b + 4
Now, the equation is:
(b+5)(2b+2) = 4b^2 + b + 4
i.e. 2b^2 + 12b+10 = 4b^2 + b + 4
i.e. 2b^2 - 11b - 6 = 0
Solving the quadratic equation: b = 6 or b = -dfrac12
Now, as the base is an integer, b = 6

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