Test time left: 35:50Choose the correct option.When a number is divided by 387, the remainder obtained is 48. If the same number is divided by 43, then the remainder obtained will be–Options30535

To find the remainder when a number is divided by 43, we can use the concept of congruence.

Given that the number leaves a remainder of 48 when divided by 387, we can express this as:

Number ≡ 48 (mod 387)

To find the remainder when the same number is divided by 43, we need to find an equivalent congruence equation.

Since 387 is not divisible by 43, we cannot directly divide both sides of the congruence equation by 43. However, we can simplify the equation by finding a common factor between 387 and 43.

The greatest common divisor (GCD) of 387 and 43 is 1. This means that 387 and 43 are relatively prime, and there is no common factor other than 1.

To simplify the congruence equation, we can use the property of modular arithmetic that states:

If a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ b + d (mod m)

We can apply this property to our congruence equation:

Number ≡ 48 (mod 387) Number ≡ 48 + 387 (mod 387) Number ≡ 435 (mod 387)

Now, we can divide both sides of the congruence equation by 43:

Number ≡ 435 (mod 387) Number ≡ 435 ÷ 43 (mod 387 ÷ 43) Number ≡ 10 (mod 9)

Therefore, the remainder obtained when the same number is divided by 43 is 10.