Let the distance from the lens to the first source be x. Then distance from lens to second source is 24−x
Applying lens formula for S2,
1v−1u=1f
1v=19−124−x
For S1,
1v−1u=1f
1v+1x=19
1v=19−1x
Equating the two,
19−124−x=19−1x
x2−24x+108=0
i.e x=6 or 18
The lesser value is x=6.