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:

**Finding remainder when a number is divided successively by 2, 3, and 5, with remainders 1, 2, and 3, and then by 30.****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?****How to find the remainder when a number, after being divided by 2, 3, and 5 with specific remainders, is further divided by 30?**