A number when divided by 143 leaves 31 as remainder. What will be the remainder
when the same number is divided by 13 ?
a)
0
b)
1
c)
3
d)
5
e)
None of these
Correct answer is option 'D'. Can you explain this answer?

Question

A number when divided by 143 leaves 31 as remainder. What will be the remainder
when the same number is divided by 13 ?

a)
0
b)
1
c)
3
d)
5
e)
None of these

Correct answer is option 'D'. Can you explain this answer?

Answer

Number is = x
x = divisor + remainder
x = 143 + 31
x = 174
when the same number is decided by 13
remainder= 174÷13
= 5 Ans.

Answer

Answer

Given Information:
- A number leaves a remainder of 31 when divided by 143.

To Find:
- The remainder when the same number is divided by 13.

Explanation:
To find the remainder when a number is divided by a divisor, we can use the concept of modular arithmetic.

Modular Arithmetic:
Modular arithmetic is a system of arithmetic for integers, where numbers wrap around after they reach a certain value called the modulus.

For example, in modular arithmetic with a modulus of 13, the numbers wrap around after they reach 13. So, 14 is equivalent to 1, 15 is equivalent to 2, and so on.

Step 1:
We are given that the number leaves a remainder of 31 when divided by 143. This can be represented as:
Number = 143k + 31, where k is an integer.

Step 2:
Now, we need to find the remainder when the same number is divided by 13. This can be represented as:
Number = 13m + r, where m is an integer and r is the remainder.

Step 3:
To find the value of r, we can equate the two representations of the number from step 1 and step 2:
143k + 31 = 13m + r

Step 4:
To simplify the equation, we can subtract 13m from both sides:
143k + 31 - 13m = r

Step 5:
Since we want to find the remainder, we need to find the smallest positive value of r. To do this, we can substitute different values of k and m and find the corresponding value of r.

Step 6:
Let's substitute k = 0 and m = 0:
143(0) + 31 - 13(0) = r
31 = r

Therefore, the remainder when the number is divided by 13 is 31 or 5 (since 31 is equivalent to 5 in modular arithmetic with a modulus of 13).

Conclusion:
The remainder when the number is divided by 13 is 5. Therefore, option D (5) is the correct answer.

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