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If the positions of the digits of a two digit no. are interchanged the number newly formed is smaller than the original number by 45. Also the ratio of new number to original number is 3 : 8. What is the original number
- a)61
- b)72
- c)94
- d)Can’t be determined
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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If the positions of the digits of a two digit no. are interchanged the...
Problem:
If the positions of the digits of a two-digit number are interchanged, the number newly formed is smaller than the original number by 45. Also, the ratio of new number to original number is 3:8. What is the original number?
Solution:
Let the original number be AB where A is the tens digit and B is the units digit. Therefore, the new number formed will be BA.
According to the question, we have:
BA = AB - 45 -----(1) (as the new number is 45 less than the original number)
Also, we know that the ratio of new number to original number is 3:8. Therefore,
BA/AB = 3/8
Multiplying both sides by 8AB, we get:
8BA = 3AB
Dividing both sides by B, we get:
8A = 3B
From equation (1), we have:
BA = AB - 45
Substituting BA = 3/8 AB in the above equation, we get:
3/8 AB = AB - 45
Solving for AB, we get:
AB = 72
Therefore, the original number is 72.
Answer:
Option (B) 72 is the correct answer.
If the positions of the digits of a two-digit number are interchanged, the number newly formed is smaller than the original number by 45. Also, the ratio of new number to original number is 3:8. What is the original number?
Solution:
Let the original number be AB where A is the tens digit and B is the units digit. Therefore, the new number formed will be BA.
According to the question, we have:
BA = AB - 45 -----(1) (as the new number is 45 less than the original number)
Also, we know that the ratio of new number to original number is 3:8. Therefore,
BA/AB = 3/8
Multiplying both sides by 8AB, we get:
8BA = 3AB
Dividing both sides by B, we get:
8A = 3B
From equation (1), we have:
BA = AB - 45
Substituting BA = 3/8 AB in the above equation, we get:
3/8 AB = AB - 45
Solving for AB, we get:
AB = 72
Therefore, the original number is 72.
Answer:
Option (B) 72 is the correct answer.
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