Inverse Proportions

Q.

A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?

1. 12 noon

2. 12:30 p.m.

3. 1 p.m.

4. 11 p.m.

Q.

If 5 persons can do a work in 10 days, then 10 people can complete the same amount of work in ____days.

1. 5

2. 20

3. 4

4. 15

Q. 9. A can do a piece of work in 25 days and B can finish it in 20 days. They work together for 5 days and then A goes away. In how many days B finish the remaining work?

Q. If $z$ varies directly with $x$ and inversely with $y$ such the constant of proportionality is equal to 1. Find the percentage change in $z$ if $x$ is increased by 5% and $y$ is increased by 20%.

1. 13.75%
2. 15%
3. 10%
4. 12.5%

Q.

If 8 men can do a job in 5 days. How much time would v10 men take to do the same job?

Q. A school has 8 periods in a day and each of 30 minutes duration. If the number of periods reduces to 6 periods a day , then find the duration of each period. (Assume the school hours remains the same)

1. 30 mins
2. 35 mins
3. 40 mins
4. 50 mins

Q.

If a person completes (1/n)^th part of the work in one day, then in how many days he will complete the whole work?

1. (n - 1)

2. n

3. n²

4. 2n

Q.

If x and y are inversely proportional, find the values of $x_1,x_2,y_{1}and{y}_2$ in the table given below :

$\begin{array}{cccccc}x& 8& x_1& 16& x_2& 80\\ y& y_1& 4& 5& 2& y_2\end{array}$

Q. If 5 men can do a piece of work in 6 days, then how many men will finish the same work in 5 days?

1. 5 men
2. 4 men
3. 8 men
4. 6 men

Q.

A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A left after some days and then B completed the remaining work in 23 days. Number of days A and B worked together is:

1. 8

2. 7

3. 12

4. 9

Q.

The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, their ages will add to 70 years. Find their present ages.

1. 15, 45

2. 10, 30

3. 20, 60

4. 18, 54

Q. If $p$ varies inversely as $q$ and directly as $r$ such that the constant of proportionality is 1. What will be the percentage change in $p$ due to an increase of 20% in $q$ and a decrease of 20% in $r$?

1. 30%
2. 33.33%
3. 32.50%
4. 34%

Q.

If 39 men can dig a canal in 15 days, in how many days can 45 men dig a canal whose length is double this canal?

Q. A contractor engaged 15 men to complete a job in 12 days. However, he soon found that 3 small boys can do the work of one man and have to be paid less. If he engaged 6 boys and 7 men to complete a job, find the time taken by them to complete the job.

Q. It is estimated that 15 workers can build a tower in 20 days. If only 10 workers are engaged for the job, then in how many days will the tower be built?

1. 28 days
2. 35 days
3. 25 days
4. 30 days

Q.

A battalion of 400 soldiers has provision for 28 days. After 8 days they are joined by 100 more soldiers, how long will the provision last now?

1. 22.4 days

2. 16.0 days

3. 19.2 days

4. 12.0 days

Q.

If X varies inversely as y and y = 60 when X=1.5 . Find X when y is = 4.5 .

Q. 26. 4 men can do as much work in 7 days as 6 women do in the same time. Find the number of days required to finish the work by 8 men and 9 women working together?

Q.

Question 96

A volleyball court is in a rectangular shape and its dimensions are directly proportional to the dimensions of the swimming pool given below. Find the width of the pool.

Q. 106.5 men or 8 women or 10 boys can complete a work in 12 days. 2 men, 4 women, and 6 boys working together will complete the work in how many days

Q. 120 men had provision for 200 days. After 5 days, 30 men died due to an epidemic. How long will the remaining food last?

Q. 12 men can dig a pond in 8 days , how many men can dig it in 6 days ?

Q.

In a college there are 10 periods per day each of 40minutes. Students were shouting to reduce the number of periods but the principal doesn't want to reduce the working hour. How will you help the principal to reduce the number of periods to 8 without changing the total working hours?

1. 55 minutes

2. 45 minutes

3. 50 minutes

4. 30 minutes

Q. 5 boys can complete a work in 10 days and 8 women can complete the work in 10 days. If all the 5 boys and 8 women work together in how many days will the work get completed?

Q. 150 workers were engaged to finish a piece of work in a certain number of days 4workers dropped the second day 4 more workers dropped the third day and so on it takes 8 more days to finish the work now find the number of days in which the work was completed

Q. On a particular day, sweets were to be equally distributed among $495$ students of a school. However, on that particular day $396$ students from a nearby school also joined them. Hence each student present on that day got four sweets less. How many sweets were distributed?

1. $4950$
2. $5445$
3. $4455$
4. $3960$
5. None of these

Q.

A plane travels $5100km$ in $6$ hours. How far will it go in $4$ hours $36$ minutes ?

Q. A factory requires 42 machines to produce a given number of articles in 63 days. How many machenics would be required to produce the same number of articles in 54 days

Q. A work can be done by 32 men in 11 days. 10 of them did not join the work. How long will it take now to complete the work?

Q.

Please explain me the derivation of the formulas of time and work