In Nuts And Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to cleaned for10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?
Answer: C Machine I: Number of nuts produced in one minute = 100 To produce 1000 nuts time required = 10 min Cleaning time for nuts = 5 min Over all time to produce 1000 nuts = 15 min. Over all time to produce 9000 = 138 min – 5 min = 133 min … (1) Machine II: To produce 75 bolts time required = 1 min To produce 1500 bolts time required = 20 min Cleaning time for bolts = 10 in. Effective time to produce 1500 bolts = 30 min Effective time to produce 9000 bolts = 30 × 6 – 10 = 170 min … (2) From (1) and (2) Minimum time = 170 minutes
Q. No. 14:
Pankaj can produce one unit in 15 days, while Bharti can do the same in 12 days. After producing one unit, working together, they received rs 90, which they distributed amongst themselves in proportional to their efficiency. If they work for 20 days, and sell the produce, then Bharti should receive
Answer: C In 1 day pankaj and Bharti together produce = 1/15 + 1/12 = 3/20 units In 20 days, together they can produce 3/20 * 20 = 3 units. From which they can fetch Rs 270 Efficiency of Bharti / Efficiency of pankaj = 15/12 = 5/4 => Share of Bharti is 5/9 * 270 = Rs 150
Q. No. 15:
Pipes A and B can fill a tank in 12 min and 16 min respectively. Both are kept open for 'n' min and then B is closed and A fills the rest of the tank in 5 min. The time 'n' after which B was closed is
Answer: D n(1/12 + 1/16) = 28n/192 => Left capacity = 1 - 28n/192 This is filled by A in 5 min and fills 1/12 in 1 min => (192-28x)/192 = 5/12 => n = 4 min
Q. No. 16:
A can build up a structure in 8 days and B can break it is 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the structure ?
Answer: D A can build the structure in 8 days. Fraction of structure built in a day by A = 1/8 similarly, fraction of structure broken by B in a day = 1/3. Amount of work dome by A in 4 days = 4/8 = 1/2. Now, both A and B together for 2 days. So, fraction of structure built in 2 days = 2(1/8 - 1/3) = -5/12 Fraction of structure still to be built = 1/2 + 5/12 = 11/12. If A takes x days to build up the remaining structure, then x/8 = 11/12 => x= 22/3 days.
Q. No. 17:
12 men cam complete a piece of work in 36 days, 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 day, how many women would be required ?
Answer: A 12 men in 36 days can do a work. 1 man in a day can do 1/(12*36) work. 8 men in 20 days can do (8*20)/(12*36) = 10/27 work. Similarly, we find that 20 women in 20 days can do 10/27 work. Remaining work = 7/27 Now, because in 60 days a work is done by 20 women. In 1 day a work done by 20* 60 women. In 4 days 7/27 work is done by (20*60*7)/(27*4) = 70 women.
Q. No. 18:
A bath can be filled by the cold water pipe in 10 min and by not water pipe in 15 min (independently each). A person leaves the bathroom after turning on both pipes simultaneously and returns at the moments when the bath should be full. Finding, however, that the water pipe has been open he now closes it. In 4 min more, bath is full. In what time would be the waste pipe empty it ?
Answer: C Waste pipe alone empties the bath in xy/(x+y) [1+ xy/t(x+y)] Here, x = 10 min, y = 15 min and t = 4 min. On putting these values, we get 15 min.