What least number must be subtracted from 2963 so that the resulting number, when divided by 9, 10 and 15, leaves a remainder of 5 in each case?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 78
A number leaving remainder 5 with 9, 10 and 15 has the form LCM \(\times k+5\). The largest such number not above 2963 needs the least subtraction.
LCM of 9, 10 and 15 \(=2\times3^{2}\times5=90\)
\(2963-5=2958\), and \(2958=90\times32+78\)
Largest suitable number \(=90\times32+5=2885\)
Number to subtract \(=2963-2885=78\)
The least number to be subtracted is 78.