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Ch - 3 Playing With Number …

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Ch - 3 Playing With Number Ex 3.3 Q6.
  • 3 answers

Pratik Zalte 3 years, 3 months ago

Hat

Simarpreet Kaur 3 years, 3 months ago

6. Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11: (a) 92 __ 389 (b) 8 __ 9484 Solutions: (a) 92 __ 389 Let ‘a’ be placed here Sum of its digits at odd places = 9 + 3 + 2 = 14 Sum of its digits at even places = 8 + a + 9 = 17 + a Difference = 17 + a – 14 = 3 + a The difference should be 0 or a multiple of 11, then the number is divisible by 11 If 3 + a = 0 a = -3 But it cannot be a negative Taking a closest multiple of 11 which is near to 3 It is 11 which is near to 3 Now, 3 + a = 11 a = 11 – 3 a = 8 Therefore the required digit is 8 (b) 8 __ 9484 Let ‘a’ be placed here Sum of its digits at odd places = 4 + 4 + a = 8 + a Sum of its digits at even places = 8 + 9 + 8 = 25 Difference = 25 – (8 + a) = 17 – a The difference should be 0 or a multiple of 11, then the number is divisible by 11 If 17 – a = 0 a = 17 (which is not possible) Now, take a multiple of 11. Let’s take 11 17 – a = 11 a = 17 – 11 a = 6 Therefore, the required digit is 6

Pranav Shinde 3 years, 3 months ago

Done
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