Question 10 - Figure it out - Page 132, 133, 134 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

Transcript

Question 10 Write a 6-digit number that it is divisible by 15, such that when the digits are reversed, it is divisible by 6.If a number is divisible by 15, it means It is divisible by 3 (sum of digits divisible by 3) It is divisible by 5 (last digit 0, or 5). Note: We choose 3 & 5 because they have no common factors Now, the reversed number should be divisible by 6 The reversed number must be even. This means the original number must start with an even digit (2, 4, 6, 8). Lets try to construct the number Start with an even number (e.g., 2), end with 5 (for div by 15 ). Fill middle with 0s for simplicity, ensuring sum is multiple of 3 . Try: 200025. Sum: 2+0+0+0+2+5=9 (Divisible by 3 ). Ends in 5 (Divisible by 5). So, 200025 works. Reverse: 520002 . Even? Yes. Sum of digits is 9 ? Yes. Thus, reverse is divisible by 6 Thus, our answer is 2,00,025