Question

Find the least number which when divided by $15$, leaves a remainder of $5$, when divided by $25$, leaves a remainder of $15$ and when divided by $35$ leaves a remainder of $25$.

• A. $515$
• B. $525$
• C. $1040$
• D. $1050$

Answer 1

The correct option is A $515$

The LCM of the numbers 15, 25 and 35 will be $75\ast 7=525$
Now, number has a remainder of 25 when divided by 35. Similarly, number has remainder 15 on dividing by 25 and remainder is 5 when divided by 15. In each case, we are 10 short of getting a zero remainder. So the desired number must be $525-10=515$
Option A