Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the numbers.
Answer
Answer (as printed):
Explanation
Let the larger number be x and the smaller number be y. Then, 3x = 4y + 3 ⇒ 3x – 4y = 3 ...(i) And, 7y = 5x + 1 ⇒ – 5x + 7y = 1 ...(ii) Multiplying (i) by 5 and (ii) by 3, we get: 15x – 20y = 15 ...(iii) and – 15x + 21y = 3 ...(iv) Adding (iii) and (iv), we get: y = 18. Putting y = 18 in (i), we get: x = 25. Hence, the numbers are 25 and 18.
Explanation as extracted from the printed page; notation may be imperfect.