Time And Work - Study Mode

[#186] Ram Lal is a renowned packager of fruits in Varanasi. He packs 70 mangoes or 56 guavas every day working 7 hours a day. His wife also helps him. She packs 30 mangoes or 24 guavas working 6 hours per day. Ram Lal has to pack 3300 mangoes and 2400 guavas with help of his wife. They works alternately, each day 10 hours. His wife started packaging firs day and works every alternate days. Similarly, Ram Lal started his work second day and and worked alternatively till the completion of the work. In how many days the work will finished?
Correct Answer

(C) 84

Explanation

Solution: Mango Packing rate of Ram Lal = $$frac{{70}}{7}$$ = 10 per hour Guavas Packing rate of Ram Lal = $$frac{{56}}{7}$$ = 8 per hour Mango Packing rate of Ram Lal's Wife = $$frac{{30}}{6}$$ = 5 per hour Guavas Packing rate of Ram Lal's Wife = $$frac{{24}}{6}$$ = 4 per hour On comparing, 8 Guavas = 10 Mangoes 1 Guavas = $$frac{{10}}{8}$$ Mangoes 2400 Guavas = $$frac{{10 imes 2400}}{8}$$ xa0 = 3000 Mangoes This means that they need to pack (6300 + 3000) Mangoes Combined Mango Packing rate of Both = 10 + 5 = 15 per hour We will take 2 days = 1 time unit. Working 10 hours a day they will pack 150 Mangoes in 1 time unit Total time taken to pack 6300 Mangoes = $$frac{{6300}}{{150}}$$xa0 = 42 time unit So, total time taken = 2 × 42 = 84 days

[#187] A group of men decided to do a job in 4 days. But since 20 men dropped out every day, the job completed at the end of the 7 th day. How many men were there at the beginning?
Correct Answer

(B) 140

Explanation

Solution: Let X be the initial number of men then, According to the question, 4X = X + (X - 20) + (X - 40) + (X - 60) + (X - 80) + (X - 100) + (X - 120) ⇒ 4X = 7X - 420 ⇒ 3X = 420 ⇒ X = $$frac{{420}}{3}$$ ⇒ X = 140 men

[#188] Two persons having different productivity of labour, working together can reap a field in 2 days. If one-third of the field was reaped by the first man and rest by the other one working alternatively took 4 days. How long did it take for the faster person to reap the whole field working alone?
Correct Answer

(A) 3

Explanation

Solution: Total efficiency of two persons = 50% [As they complete work in 2 days. ] First Person completes work = $$frac{1}{3}$$ = 33.33% [In 2 days] Rest work will be completed by Second man = $$frac{2}{3}$$ = 66.66% [In 2 days] So, efficiency of second person is greater. Efficiency of second person = $$frac{{66.66}}{2}$$xa0 = 33.33% per day Then, Second person will complete whole work in, = $$frac{{100}}{{33.33}}$$xa0 = 3 days.

[#189] A group of workers was put on a job. From second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?
Correct Answer

(D) 10

Explanation

Solution: Let initially X number of workers be there. Now,
Using work equivalence method, X + (X - 1) + (X - 2) + . . . . . + 1 = X × 55% of X $$frac{{{ ext{X}} imes left( {{ ext{X}} + 1}
ight)}}{2} = frac{{5{ ext{X}}}}{{100}}$$ [series is in AP. Sum of AP = {No. of terms (first term + last term)/2}] X = 10 workers.

[#190] A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40, 000 litres of petrol is used daily, the supply fails in 90 days. If 32, 000 litres of petrol used daily, it fails in 60 days. How much petrol can be used daily without the supply ever failing?
Correct Answer

(B) 56000 litres

Explanation

Solution: Let X litres be the per day filling and L litres be the capacity of the reservoir, then 90X + L = 40000 × 90 ----------- (1) 60X + L = 32000 × 60 ----------- (2) Solving the equation, X = 56000 litres Thus, 56000 litres per day can be used without the failure of supply.