If abc + abc + abc = ccc Given : - that a,b and c are single digit natural numbers. - abc and cc

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08 Mar 2017 Find the value

If abc + abc + abc = ccc
Given :
- that a,b and c are single digit natural numbers.
- abc and ccc represents a 3 digit number

Find the value of (a*b*c)- (a*b) – (a*c) - a - b - c ?

OPtion

1) 0
2) 3
3) 7
4) 10
5) 13
6) 17
7) 21
8) 25
9) 27
10)29

Solution

3*(abc) = ccc
300a+30b+3c = 100c+10c+c
300a+30b = 108c
100a + 10b = 36c
Looking at RHS, we can see that C would be greater than 3 to make LHS postive
So for C=4 and a=1
100+10b = 144
b = 4.4
So for C=5 and a=1
100+10b = 180
b = 8
so a = 1, b= 8 and c=5
abc- ab - ac - a - b - c = 40 - 8 - 5 - 1 - 8 - 5 = 13

Option 5)

Correct Option: 5 Best Solution (13)

Dr.Dipin Singh   8 years AGO

abc+abc+abc=ccc

3c=10+c
2c=10
c=5
abc=555/3=185
a=1
b=8
c=5
(a*b*c)-(a*b)-(a*c)-a-b-c = (1*8*5)-(1*8)-(1*5)-1-8-5= 13

Like? Yes (9) | No (1)  

G.S.Kantharao   8 years AGO

The number abc is 185
185+185+185 =555
(a*b*c)-(a*b)-(a*c)-a-b-c
(1*8*5)-(1*8)-(1*5)-1-8-5=13
Hence my choice is 5.

Like? Yes (7) | No (1)  

Pragati Rode   8 years AGO

3*abc = ccc
abc = ccc/3
we get a=1,b=8 and c=5

putting all these values in eq
we get answer 13

so option is 5

Like? Yes (3) | No (3)  

Mukund Manohar   8 years AGO

abc+abc+abc = ccc
=>3abc = ccc
abc = ccc/3
By hit & trial method,ccc= 555
So, abc = 555/3 = 185
a= 1,b = 8,c = 5
(a*b*c) - (a*b) - (a*c) - a - b - c = 40-8-5-1-8-5 = 13

Like? Yes (1) | No (1)  

Venkatesh kadali   8 years AGO

185+185+185 = 555
so a=1 b=8 c=5
(a*b*c)-(a*b)-(a*c)-a-b-c = (1*8*5)-(1*8)-(1*5)-1-8-5
=13
so answer is option 5

Like? Yes | No (1)  

Azim Uddin Siddiqui   8 years AGO

given abc+ abc+abc=ccc; a,b,c are natural single digit nos. for unit place only 2 logical values possible only 0+0+0=0 or 5+5+5=15 gives same digit in unit's place ; so c=5; since v have a carry of 1 in the unit's place b can be any single digit number which when added thrice gives 4 in the unit's place so when 1 which is carried is added it makes the answer in unit place as 5 which is required. this is possible with 8 .8+8+8= 24+ 1(carry in the ten's place)=25 : now in the hundred's place there is a carry of 2 so a will be 1 .1+1+1=3+2=5, so the numer abc is 185. solving for given equation by putting values of a,b & c V get (a*b*c)-(a*b)-(a*c)-a-b-c=13

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THANUKU DEEKSHITH   8 years AGO

a=1 b=8 c=5
such that 3abc=ccc
3*185=555
185=555/3
this are the only single digit natural numbers which satisfies the above equation
therefore (a*b*c)-(a*c)-(a*b)-a-b-c=40-8-5-1-8-5=13

Like? Yes | No (1)  

nilay gandhi   8 years AGO

C=5
B=8A=1
so from given expression 13 is answer

Like? Yes | No (1)  

Devendra Marghade   8 years AGO

abc + abc + abc = ccc gives a=1, b=8, c=5
So (a*b*c) - (a*b) -(a*c) - a -b -c = 40 - 8 - 5 - 1 - 8 - 5=13
Option 5)

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Harsh Poddar   8 years AGO

abc=185
a=1,b=8,c=5
Putting the values in the equation final result=13
Option 5

Like? Yes | No (2)  

Naga   8 years AGO

Last digit remains same after adding the three identical numbers abc.
So last digit is 5 and the sum is 555
So abc = 185
ans = (1*8*5)-(1*8)-(1*5) -1-8-5
= 13

Like? Yes | No (2)  

DEEPALI AGARWAL   8 years AGO

since a,b,c are 3 different digits...
so, a,b,c can be any digit from 1-9.
taking it for RHS=
ccc ={ 111,222,333,444,555,666,777,888,999}
now considering,
abc +abc+abc=ccc
c+c+c=c, which can be possible only in case of 5.
where 5+5+5=15
so, c=5
which gives 1 as carry now,
I.e b+b+b+1=_5
so 8+8+8+1=25
b=8, carry=2
a+a+a+2=_5
1+1+1+2=5
so,a=1...
there it is a=5, b=8,c=1.
(a*b*c)-(a*b)-(a*c)-a-b-c= (1*8*5)-(1*8)-(1*5)-1-8-5=13

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Sharan Raj   8 years AGO

a=1;b=8;c=5;
185*3=555
And substituting the values in the given equation gives the answer 13

Like? Yes | No (3)