Question
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 and got the remainders 4, 8, 12 respectively. What would have been the remainder if he had divided the number by 585?
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 and got the remainders 4, 8, 12 respectively. What would have been the remainder if he had divided the number by 585?
Answer: Option D
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Answer : Option D
Explanation :
Let P be the number
Given that
P ÷ 5 = Q, remainder = 4
Q ÷ 9 = R, remainder = 8
R ÷ 13 = 1, remainder = 12
Hence R = 1 × 13 + 12 = 25
Q = 9R + 8 = (9 × 25) + 8 = 225 + 8 = 233
P = 5Q + 4 = (5 × 233) + 4 = 1165 + 4 = 1169
P ÷ 585 = 1169 ÷ 585 = 1, remainder = 584
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