Bright Zoom Maths

Solved Problems - Pipes And Cisterns 1. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 min. How long will the waste pipe take to empty the full cistern? Answer: 10 minutes Explanation: Work done by a waste pipe in 1 minute = 1 / 20 - ( 1 / 12 + 1 / 15 ) = ( 3 - 5 - 4 ) / 60 = ( -6 / 60 ) = -1 / 10 ∴ Waste pipe will empty the full cistern = 10 minutes 2. Two pipes X and Y can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? Answer: 18 hours Explanation: Part filled by X in 1 hour = 1 / 30 Part filled by Y in 1 hour = 1 / 45 Part filled by (X+Y) in 1 hour = 1 / 30 + 1 / 45 = ( 3 + 2 ) / 90 = 5 / 90 = 1 / 18 ∴ Both the pipes together will fill the tank = 18 hours 3. An electric pump can fill a tank in 2 hours. Because of a leak in the ...

Aptitude puzzle What is the four-digit number (no zeros) in which the third digit is the number of ′wind′ the first digit is one-half of the third, the second digit is double the third and the last digit is one-half the sum of the first three? Answer: 2847 Explanation: Wind = 4 letters The third number = 4 First digit = 1 / 2 of the third digit = ( 1 / 2 ) * 4 = 2 Second digit = Double the third digit = 2 * 4 = 8 Fourth digit = 1 / 2 of the sum of first three digits = ( 1 / 2 ) * ( 2 + 8 + 4 ) = ( 1 / 2 ) * 14 = 7 Four digit number = 2847

Aptitude Solved Problems Bright Zoom Maths, 1. 36 men can complete a piece of work in 18 days. In how many days will 24 men complete the same work? Answer:  27 days Explanation: Let the required number of days be x. ⇒ Less men, More days ( ∴ Indirect propportion ) ⇒ 24 : 36 :: 18 : x ⇒ 24x = 36 * 18 x = ( 36 * 18 ) / 24 x = 9 * 3 x = 27 days ∴ 27 days to complete the work 2. In a lottery, there are 25 prizes and 10 blanks. A lottery is drawn at random. What is the probability of getting a prize? Answer:  5 / 7 Explanation: Total number of outcomes possible, n ( S ) = 25 + 10   = 35 Total number of prize, n ( E ) = 25 p ( E ) = n ( E ) / n ( S ) = 25 / 35 .  = 5 / 7 ∴ Required probability = 5 / 7 3. Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 360. Find their H.C.F. ? Answer:  30 Explanation: Let HCF of the numbers be x Let the numbers be 2x, 3x and 4x. LCM of 2x, 3x and 4x = 12x ⇒ 12x = 360 x = ...