A tank has 3 pipes attached to it. the pipes are of square cross section with sides 3cm, 9cm and 6cm. If the smallest pipe takes 16 minutes to fill the tank, how long (in minutes) will it take for the three pipes together to fill the tank?(Amount of water flowing per minute through each pipe is proportional to the square of the side.)
Answer: D The rate of flow is proportional to the area of cross section of the inlet pipe. Since rate of flow is inversely proportional to the time taken, the time taken by a pipe to fill the tank is inversely proportional to the area of cross section. Cross-section area of the 3 pipes are 9cm2, 81cm2 and 36cm2 Given that 9cm2 -------> 16 minutes => 81cm2 -------------> 16/9 min and 36cm2 -------------> 16/4 min Fraction of the tank filled per minute = 1/16 + 9/16 + 4/16 = 14/16 Hence the time taken by the tank to get filled = 16/14 = 8/7 minutes
Q. No. 26:
A and B borrowed a tractor for 23 days. A ploughed 12 acres per day for a certain number of days and then Bused it to plough 15 acres per day for the remaining days. If they paid Rs 3,000 and Rs 2,000 respectively, for how many days did A use the tractor?
Answer: B Expenses proportional to (Number of acres ploughed per day) (Number of days). Assuming A used the tractor for 'd' days, the ratio of A's to B's expenditure is => 12d : (23-d)15 This is given to be equal to 3000 : 2000 or 3:2 Thus, 12d : (23-d)15 = 3:2 Thus d = 15. Therefore A's used the tractor for 15 days.
Q. No. 27:
Jay and Anup can do a job, each working alone in 30 and 15 days respectively. Jay started the work and after a few days, Anup joined him. They completed the work in 18 days from the start. After how many days did Anup join A?
Answer: C Since Jay does 1/30 th of the work in one day, total work done by Jay in 18 days = 18/30 =3/5. Remaining 2/5 th work was done by Anup. Since Anup does 1/15th of the work = (2/5)/(1/15) = 6 days. So, Anup joined Jay after (18 - 6) = 12 days.
Q. No. 28:
water flows into a reservoir which is 200 m long and 150 m wide, through a pipe of cross-section (0.3m X 0.2m) at 20kmph. In what time will the water level be 8?
Answer: D Volume of water collected in the tank in 1 hour => 0.3*0.2*20*1000 = 1200 m cubic If after t hours, the water is at height of 8m, 1200t = 200*150*8 => t = 200.
Q. No. 29:
A, B and C, can complete a piece of work individually in 15, 30 and 40 days respectively. They started the work together and the A and B let 2 days and 4 days before the completion of the work respectively. In how many days was the work completed?
Answer: D Let it takes x days to complete the work The A worked for (x-2) days, B for (x-4) days and C's for x days. x/40 + (x-4)/30 + (x-2)/15 =1 => x =152/15.
Q. No. 30:
Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages.
Answer: B Assume there are 360 units of work (LCM of 40, 60 and 12). Hence, A,B and C can do 4,9 and 30 units per day or together 43 units every 3 days. So In 24 days, 43*8 = 344 units of work is completed. In the next 2 days, 13 units are completed and on 27th day, C takes (1/10) of a day to finish the rest. So, A and B worked for 9 days each and have hence put in 36 and 81 units respectively, and the rest of the 243 units is put in by C. The wages shall also be distributed in the same ratio as Rs 36, Rs 81 and Rs 243.
