The difference of two numbers is 1365. On dividing the larger number by the…
2025
The difference of two numbers is 1365. On dividing the larger number by the smaller , we get 6 as quotient and 15 as reminder . What is the smaller number ?
- A.
240
- B.
270
- C.
295
- D.
360
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Let the larger number be a and the smaller number be b.
From the difference: a − b = 1365.
From the division: dividing the larger by the smaller gives quotient 6 and remainder 15, so a = 6b + 15.
Substitute the second equation into the first: (6b + 15) − b = 1365, which simplifies to 5b + 15 = 1365.
Solve for b: 5b = 1365 − 15 = 1350, so b = 1350 ÷ 5 = 270.
Check: larger a = 6×270 + 15 = 1635; difference 1635 − 270 = 1365 (matches). Also remainder 15 < divisor 270, so the division statement is valid.
Answer: 270