You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

[Q]: Question: A certain car dealership offers its newest model in ten exterior and six interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?

 Option A: 45

 Option B: 81

 Option C: 90

 Option D: 10!/2!

 Option E: 36
[A]: Option E


[Q]: Question: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?

 Option A: 14 min 19 sec

 Option B: 14 min 42 sec

 Option C: 14 min 20 sec

 Option D: 14 min 40 sec

 Option E: 14 min 10 sec
[A]: Option D


[Q]: Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?

 Option A: 12:17:16

 Option B: 12:15:16

 Option C: 13:15:16

 Option D: 12:35:16

 Option E: 12:15:18
[A]:
Option B