Latest Elitmus Aptitude Question SOLUTION: In number system 541 * 21 =20222 , find 421 in decimal number system

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In number system 541 * 21 =20222 , find 421 in decimal number system

Asked In Elitmus Shivangi vaish (11 years ago)

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kishan kumar  (11 years ago)

the no. in x digit no. in N th base would be
n=N^x-N^(x-1)
so
541*21= 11361(5 digit no.)
20222(five digit no.)
so by formula
5=N^5-N^4;
5=N^4(N-1)
so if N-1=5
N=6
So base would be 6
now we have to convert 421 to decimal
so
4*6^2+2*6+1*6^0
=144+12+1
=157
bhai yahi hoga answer

Is this solution Helpfull? Yes (11) | No (5)  

jayakishore  (11 years ago)

pls can any one explain this

Is this solution Helpfull? Yes (3) | No   

chandan kumar  (11 years ago)

formation of nos.btwn 100 and 200
101
110 112
121 123
132 134
143 145
154 156
165 167
176 178
187 189
198
so total 18 nos. btwn 100 and 200 hundred (see pattern of the above nos. its simple)
now from 201 to 300
202
211 213
220 224
231 235
242 246
253 257
264 268
275 279
286
297
so total 17 nos. btw 201 and 300. see last two rows decreasing
hence similarly btw 301 to 400 one more no will decrease in the row btwn 370 to 380 leading to total of 16 nos in btw 301 to 400.
so total sum =18+17+16= 51
it's correct

Is this solution Helpfull? Yes (2) | No   

himanshu dadhich  (9 years ago)

here the no given that is

541 and 21 both are of the same base as of the no 20222 is,so

firstly find the base
which is given by formula with x digit no. in N base

n=N^x-N^(x-1)
here the digit having 5 no. so

5=N^4(N-1)

so N-1=5
N=6

After converting the numbers in decimal number system
the actual no are
206*13=2678


so similarly converting the given no. in decimal no. system

4*6^2+2*6^1+1*6^0

which gives no as

157

Is this solution Helpfull? Yes (2) | No   

ravi gangwar  (11 years ago)

which type que. is this can anybdy explain it?

Is this solution Helpfull? Yes (1) | No   

rishabh singh bisht  (11 years ago)

SOMETHING WRONG IN QUESTION. Unit digit must be 1.

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

vidhi prakash  (11 years ago)

17702
541-421*21

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abc  (11 years ago)

i think the questn is like 542 * 21 =20222 , find 421 in decimal number system?

from the given numbers we can find the base =6
so 421 in decimal will be 111.

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

Anuj Gupta  (7 years ago)

Question is wrong .
541 base 6 = 205 base 10
21 base 6 = 13 base 10

205 * 13 = 2665 base 10

now converting base 10 to base 6 means
2665 base 10 = 20201 base 6

show this question is wrong.

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abc  (11 years ago)

@shivangi
r u sure abt the questn.
unit digit of either 541 or 21 should be 2
or
unit digit of rhs should be 1

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KAPIL DEV  (11 years ago)

pls yr solve this

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vinod  (11 years ago)

no clarity in que......

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