two fill taps a and b can separately fill a cistern in 45 and 40 minutes respectively . they started to fill a cistern together but tap a is turned off after few minutes and tap b fills the rest part of cistern in 23 minutes . after how many minutes , was tap a turned - off ?
let a was turned off after x min . then , cistern filled by a in x min + cistern filled by b in ( x + 23 ) min = 1 ⇒ x / 45 + x + 23 / 40 = 1 ⇒ 17 x + 207 = 360 ⇒ x = 9 min . answer a
divide(subtract(const_1, multiply(speed(const_1, 40), 23)), add(speed(const_1, 45), speed(const_1, 40)))