Problem: two pipes a and b can fill a cistern in 10 and 15 minutes respectively . both fill pipes are opened together , but at the end of 3 minutes , ‘ b ’ is turned off . how much time will the cistern take to fill ?
Rationale: in one min , ( a + b ) fill the cistern = 1 ⁄ 10 + 1 ⁄ 15 = 1 ⁄ 6 th in 3 min , ( a + b ) fill the cistern = 3 ⁄ 6 = 1 ⁄ 2 th remaining part = 1 - 1 ⁄ 2 = 1 ⁄ 2 ∵ 1 ⁄ 10 th part filled by a in one min . ∴ 1 ⁄ 2 nd part filled by a in 10 × 1 ⁄ 2 = 5 min . ∴ total time = 3 + 5 = 8 min . answer b
annotated_formula: add(multiply(10, subtract(const_1, multiply(add(inverse(10), inverse(15)), const_3))), 3)