A number when successively divide by 3, 5 and 8 leaves remainders 1, 4 and 7 respectively. Find the respective remainders if the order of divisors be reversed.Options :A] 5, 4, 2B] 6, 4, 2C] 1, 1, 3D] None of these

This problem can be solved using the Chinese Remainder Theorem.

Step 1: The first step is to find a number that when divided by 3 leaves a remainder of 1. This number is 4 (since 3*1 + 1 = 4).

Step 2: Next, we need to find a number that when divided by 5 leaves a remainder of 4. We start with the number we found in step 1, which is 4, and add multiples of 3 (the first divisor) until we find a number that satisfies this condition. This number is 14 (since 5*2 + 4 = 14).

Step 3: Finally, we need to find a number that when divided by 8 leaves a remainder of 7. We start with the number we found in step 2, which is 14, and add multiples of 15 (the product of the first two divisors) until we find a number that satisfies this condition. This number is 74 (since 8*9 + 7 = 74).

So, the number that when successively divided by 3, 5 and 8 leaves remainders 1, 4 and 7 respectively is 74.

Now, if we reverse the order of the divisors and divide 74 by 8, 5 and 3, the remainders will be:

74 mod 8 = 2 (74 - 2)/8 mod 5 = 9 mod 5 = 4 ((74 - 2)/8 - 4)/5 mod 3 = 1 mod 3 = 1

So, the respective remainders if the order of divisors be reversed are 2, 4 and 1. Therefore, the answer is D] None of these.

This problem can be solved using the Chinese Remainder Theorem.

Step 1: The given problem can be written as: x ≡ 1 (mod 3) x ≡ 4 (mod 5) x ≡ 7 (mod 8)

Step 2: Find the product of the divisors: 358 = 120

Step 3: Divide the total product by each divisor to find the individual products: 120/3 = 40 120/5 = 24 120/8 = 15

Step 4: Find the multiplicative inverse of each individual product with respect to the original divisor: 401 ≡ 1 (mod 3) 241 ≡ 1 (mod 5) 15*7 ≡ 1 (mod 8)

Step 5: Multiply the remainder of each original congruence by the product found in step 3 and the multiplicative inverse found in step 4: 1401 = 40 4241 = 96 7157 = 735

Step 6: Add the results from step 5 and find the remainder when divided by the product of the divisors (from step 2): (40 + 96 + 735) mod 120 = 71

So, the number is 71.

Now, if we reverse the order of divisors and divide 71 by 8, 5, and 3, we get the remainders as follows:

71 mod 8 = 7 (71-7)/8 mod 5 = 4 ((71-7)/8 - 4)/5 mod 3 = 1

So, the remainders when the order of divisors is reversed are 7, 4, and 1. Therefore, the answer is D] None of these.