a) 29

b) 19

c) 23

d) 13

correct answer is: c) 23

Explanation

If we start from the end because it is a case of successive division (here number 5), then we get:
5x+3 is the number which will leave a remainder of 3 after divided by 5 .
3\left(5x+3\right)+2 is the number which will leave a remainder of 2 after divided by 3 .
2\{3\left(5x+3\right)+2\}+1 is the number which will leave a remainder of 1 after divided by 2 .
On opening the brackets, we get:
2\{3\left(5x+3\right)+2\}+1
\rightarrow 2\left(15x+9+2\right)+1
\rightarrow 30x+18+4+1
\rightarrow 30x+23
Now if we divide this number by 30 then we get:
\large\frac{30x+23}{30}
\rightarrow x+23

So, here we find that dividing the number by 30 leaves 23 as the remainder.
\therefore If we divided the number by 30 then the remainder will be 23 .
And the number is \left(30+23\right)
\rightarrow 53
Ans: The number is 53 which divided by 2, 3 and 5 in succession the remainders are 1, 2 and 3 respectively and if it is divided by 30 then the remainder will be 23.

Alternative phrasings for this particular query are:

1. Finding remainder when a number is divided successively by 2, 3, and 5, with remainders 1, 2, and 3, and then by 30.
2. What will be the remaining value when a number, with remainders 1, 2, and 3 in divisions by 2, 3, and 5 respectively, is divided by 30?
3. How to find the remainder when a number, after being divided by 2, 3, and 5 with specific remainders, is further divided by 30?