Question

A number when successively divided by 5.6 and 7 leaves remainder 3, 2 and 4 respectively. When the order of successive division gets reversed then find the remainders. ​

Answer 1

Answer:

When the order of successive division gets reversed then the respective remainders are 0,1, 3.

Step-by-step explanation:

Let the number(dividend) be D, and the quotients  that will be obtained after the successive divisions be q, r, & s respectively.

Dividend = Divisor * Quotient + Remainder,

Using this rule, we get

D = 5q + 3

q = 6r + 2

r = 7s + 4

Passing value of r in q, & then value of q in D, we get

D = 5[6(7s + 4) + 2] + 3

=> D = 5(42s + 26) + 3

=> D = 210s + 133, where s can be any whole number.

Successively dividing D by 7, 6, and 5 (reversing the previous order), we get

D/7 = (210s + 133)/7, which gives quotient = (30s + 19) & remainder = 0

Then, (30s + 19)/6 gives quotient = (5s + 3) & remainder = 1

Finally, (5s + 3)/5 gives quotient = s & remainder = 3

Therefore, the respective remainders are 0,1, 3.