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Question Id : 11647 | Context :NIMCET 2024

Question

Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20, leaves the remainders 4, 5, 10, and 15, respectively
🎥 Video solution / Text Solution of this question is given below:

Find the smallest number which when divided by 9, 10, 15 and 20 leaves remainders 4, 5, 10 and 15 respectively.

✅ Solution:

Let the number be x.

  • x \equiv 4 \mod 9 \Rightarrow x - 4 divisible by 9
  • x \equiv 5 \mod 10 \Rightarrow x - 5 divisible by 10
  • x \equiv 10 \mod 15 \Rightarrow x - 10 divisible by 15
  • x \equiv 15 \mod 20 \Rightarrow x - 15 divisible by 20

So, x + 5 is divisible by LCM of 9, 10, 15, 20

LCM = 2^2 \cdot 3^2 \cdot 5 = 180

x + 5 = 180 \times 2 = 360 \Rightarrow x = 355

? Final Answer: \boxed{355}


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