When a number is divisible by 7, its general form can be written as, 7K.
But this number leaves a remainder of 2 when divided by 7, hence its general form is, 7K+2.
But the same number gives a remainder of 3, when divided by 5, Therefore, when we subtract 3 from the general form, 7K-1, is now divisible by 5.
Now we try different possible integral values for K, 0,1,2…..we can find that K=3 is the one satisfying our criteria. Therefore we put k=3 in our general form, 7K+2, to get 23 as our number.
Now this number when divided by 35 will definitely leave 230 as the remainder itself. Hence 23 is our ans.