Question

13. A boy running up a stair case finds the
when he goes up two steps at a time there is
one step left over, when he goes up three
steps at a time there are 2 steps left over
and when he goes up 4 steps at a time there
are 3 steps left over. Find the number of
stairs which is somewhere between 90 and
100.​

Answer 1

Answer: 95

Step-by-step explanation:

Had there been one more step, the number of steps would be an exact multiple of 2,3 as well as 4.

So LCM of 2,3,4 = 12

The highest common multiple in the range 90 - 100 will be 12 × 8 = 96.

therefore the number of steps = 96 - 1 = 95