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if (75-a)(75-b)(75-c)(75-d)(75-e)=112299 then a+b+c+d+e=?

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TCS Other Question

2 workers, one young and one old, live together and work at the same office. It takes 20 minutes for the young man to walk to office. The old man takes 30 minutes for the same distance. When will the young man catch up with the old man, if the old man starts at 10:00 a.m. and the young man start 10:05 a.m.? What is $sumlimits_{K = 0}^{28} {{K^2}(_K^{28}C)} $ where $_K^{28}C$ is the number of ways of choosing k items from 28 items?
a. 406 * ${2^{27}}$
b. 306 * ${2^{26}}$
c. 28 * ${2^{27}}$
d. 56 * ${2^{27}}$