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# Application of Inverse Proportion

If 20 persons can do a piece of work in 7 days then calculate the number of persons require to complete the work in 28 days

• Related Questions

A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

 A) 11 days B) 12 days C) 13 days D) 14 days

Explanation:

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.

Number of days required for this initial work = 7 days.

Thus, the total numbers of days required = 4 + 7 = 11 days.

Subject: Time and Work - Quantitative Aptitude - Arithmetic Ability

15

A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6 AM and they work alternately for one hour each. When will the work be completed?

 A) 4 days B) 5 days C) 6 days D) 7 days

Explanation:

Work donee by A and B in the first two hours, working alternatively = First hour A + Second hour B = (1/4) + (1/12) = 1/3.

Thus, the total time required to complete the work  = 2 (3) = 6 days

Subject: Time and Work - Quantitative Aptitude - Arithmetic Ability

6

Two pipes A and B can fill a tank in 24 hours and $\inline \frac{120}{7}$ hours respectively. Harihar opened the pipes A and B to fill an empty tank and some times later he closed the taps A and B , when the tank was supposed to be full. After that it was found that the tank was emptied in 2.5 hours because an outlet pipe "C" connected to the tank was open from the beginning. If Harihar closed the pipe C instead of closing pipes A and B the remaining tank would have been filled in :

 A) 2 hours B) 8 hours C) 6 hours D) 4 hours

Explanation:

Efficiency of Inlet pipe A = 4.16%                              $\inline (\frac{100}{24})$

Efficiency of Inlet pipe B = 5.83%                              $\inline (\frac{100}{120/7})$

$\inline \therefore$ Efficiency of A and B together = 100 %

Now, if the efficiency of outlet pipe be x% then in 10 hours the capacity of tank which will be filled = 10 *  (10 - x)

Now, since this amount of water is being emptied by C at x% per hour, then

$\inline \frac{10\times (10-x)}{x}=2.5 \: hours \Rightarrow$ x = 8%

Therefore, in 10 hours 20% tank is filled only. Hence, the remaining 80% of the  capacity will be filled by pipes A and B  in 80/10 = 8 hours

Subject: Time and Work - Quantitative Aptitude - Arithmetic Ability

11

There are three boats B1, B2 and B3 working together they carry 60 people in each trip. One day an early morning B1 carried 50 people in few trips alone. When it stopped carrying the passengers B2 and B3 started carrying the people together. It took a total of 10 trips to carry 300 people by B1, B2 and B3. It is known that each day on an average 300 people cross the river using only one of the 3 boats B1, B2 and B3. How many trips it would take to B1, to carry 150 passengers alone?

 A) 15 B) 30 C) 25 D) 10

Explanation:

Combined efficiency of all the three boats = 60 passenger/trip

Now, consider option(a)

15 trips and 150 passengers means efficiency  of B1 = $\inline \fn_jvn 10\frac{p}{t}$

which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (10-5 = 5) in which B2 and B3 together carried remaining 250 (300 - 50 = 250) Passengers.

Therefore the efficiency of B2 and B3 = $\inline \fn_jvn \frac{250}{5}=50\frac{p}{t}$

Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct.

Subject: Time and Work - Quantitative Aptitude - Arithmetic Ability

6

A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):

 A) 200, 250, 300 B) 300, 200, 250 C) 200, 300, 400 D) None of these

Explanation:

A's 5 days work = 50%

B's 5 days work = 33.33%

C's 2 days work = 16.66%          [100- (50+33.33)]

Ratio of contribution of work of A, B and C = $\inline \fn_jvn 50:33\frac{1}{3}:16\frac{2}{3}$

= 3 : 2 : 1

A's total share = Rs. 1500

B's total share = Rs. 1000

C's total share = Rs. 500

A's one day's earning = Rs.300

B's one day's earning = Rs.200

C's one day's earning = Rs.250