Direct and Inverse Proportions

If $x$ and $y$ vary directly and $x = 15$ when $y = 5$, find $y$ when $x = 60$.

$2$ liters of juice are needed for $8$ people. How many liters are needed for $20$ people?

If $3$ tickets for a movie cost ₹$450$, what is the cost of $7$ tickets?

A map scale is $1:1,000,000$. If the distance between two cities on the map is $5$ cm, what is the actual distance in km?

If $x$ and $y$ vary directly and $x=36$ when $y=60$, what is the value of $y$ when $x=24$?

A car covers $120$ km in $2.5$ hours. How long will it take to cover $432$ km at the same speed?

An extension spring stretches $12$ cm when a weight of $15$ kg is hung from it. How much will it stretch if a weight of $25$ kg is hung?

If $12$ meters of fabric cost ₹$2,700$, how many meters of the same fabric can be bought for ₹$5,625$?

A model of a ship is made to a scale of $1:250$. If the length of the model is $1.2$ m, what is the actual length of the ship?

If $x$ and $y$ are in direct proportion such that $x_1/y_1 = x_2/y_2$, and $x_1 = 0.4$, $y_1 = 1.6$, $x_2 = 2.5$, find $y_2$.

If $6$ men can construct a shed in $4$ days, how many days will it take $8$ men to construct the same shed?

$40$ men can finish a job in $26$ days. How many men are required to finish the same job in $20$ days?

$12$ pipes can fill a tank in $2$ hours. How long will it take $3$ pipes to fill the same tank?

If $x$ and $y$ vary inversely and $x = 3$ when $y = 16$, find the value of $y$ when $x = 4$.

If $x$ and $y$ are inversely proportional, what happens to $y$ if the value of $x$ is doubled?

The product of $x$ and $y$ is constant. If $x=15$ when $y=4$, find $y$ when $x=12$.

$4$ men can paint a fence in $6$ hours. How many hours will it take $3$ men to paint the same fence?

A cistern has $3$ inlet pipes that can fill it in $12$ hours. If $2$ more pipes of the same capacity are added, but each pipe's flow is restricted to $80\%$ of its original capacity due to a blockage, how many hours will it take to fill the cistern?

If $y$ varies inversely as $x^2$. If $x$ is increased by $50\%$, what is the percentage decrease in $y$?

The force $F$ required to loosen a nut is inversely proportional to the length $L$ of the wrench. If a force of $60\text{ N}$ is required with a $20\text{ cm}$ wrench, what length of wrench is needed to loosen the same nut with a force of $40\text{ N}$?

If $10$ oranges cost ₹$80$, what is the cost of $1$ dozen oranges?

If $14$ men can dig a trench in $6$ days, how many men can dig it in $4$ days?

In a model of a ship, the mast is $9$ cm high, while the mast of the actual ship is $12$ m high. If the length of the ship is $28$ m, how long is the model ship?

A prize of ₹$6,000$ is to be divided equally among winners. If there are $3$ winners, each gets ₹$2,000$. If there are $5$ winners, how much will each get?

If 6 copies of a specific textbook cost ₹900, how much will 10 copies of the same textbook cost?

If 20 men can build a 50m long wall in 10 days, how many days will 25 men take to build a 75m long wall?

$A, B$ and $C$ can together finish a work in 4 days. $A$ alone can do it in 12 days and $B$ in 18 days. How many days will $C$ alone take to finish the work?

A contractor undertook to do a certain piece of work in $9$ days and employed a certain number of men. But $6$ of them being absent from the very first day, the rest could finish the work in $15$ days. The number of men originally employed were:

A and B together can do a work in $8$ days. B and C together in $6$ days, while C and A together in $10$ days. If they all work together, the work will be completed in:

A builder decided to build a farmhouse in $40$ days. He employed $100$ men in the beginning and $100$ more after $35$ days and completed the construction in stipulated time. If he had not employed the additional men, how many days behind it would have been finished?