Questions & Answers

Question

Answers

( a ) 28

( b )27

( c ) 26

( d ) 24

Answer
Verified

In this question it is given that there is a six digit number abcdef and when this number is multiplied with 6 then the resulting number is also a six digit number and is defabc. Basically, we have to find the sum of all six numbers that is a + b + c + d + e +f

So, we can denote above statement as

$ 6\cdot (abcdef)=defabc $

As a, b, c, d, e, f are numbers so we can write abcdef as $ 1000\cdot abc+def $ and defabc as $ 1000.def+abc $.

$ 6\cdot (1000\cdot abc+def)=1000.def+abc $

On solving by opening brackets we get

$ 6000\cdot abc+6def=1000.def+abc $

Taking terms of abc on left side and terms of def on right side, we get

$ 6000\cdot abc-abc=1000.def-6def $

On solving, we gte

$ 5999\cdot abc=994\cdot def $

On simplifying coefficients of terms abc and def, we gte

$ 857\cdot abc=142\cdot def $

Now, just see the pattern, what we see is on left side the, in 857abc, 857 denotes def and on right hand side, in 142def, 142 denotes abc.

So, abc = 142 and def = 857

Then, abcdef = 142857

So, a + b + c + d + e +f = 1 + 4 + 2 + 8 + 5 +7 = 27