Let be the greatest number that will divide 1305,4665,6905, leaving the same remainder in each case. Then the sum of the digits in is.

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answer is A.

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Detailed Solution

Concept- Consider the HCF as being necessary to answer anyQuestion involving the greatest divisor.
Given, let N be the biggest number that will divide each of the following by the same remainder: 1305, 4665, and 6905.
The numbers can therefore be expressed as;

Where
x, y, z are integers.
Now, Equation (ii) - Equation (i) :
$Question Image$

Similarly, Equation (iii) - Equation (ii) :

Also, Equation (iii) - Equation (i) :

So from equation (iv), (v) and (vi);
We can say that 3360,2240 and 5600 have

as one of their common factors.
Product of all common factors is referred to as the HCF.
So, for finding

we first have to find the value of HCF of 3360,2240 and 5600 and if the HCF is smaller than the smallest number initially mentioned in theQuestion i.e. 1305 which is

.
Using method of factorisation for finding HCF;

Also, 1120 is smaller than 1305 .

Now, the sum of the digits of

.
Hence, the answer is option (1).
Syllabus: CBSE

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