R. D. Sharma Solutions for Chapter: Direct and Inverse Variations, Exercise 2: EXERCISE

$1200$ soldiers in a fort had enough food for $28$ days. After $4$ days, some soldiers were transferred to another fort and thus the food lasted now for $32$ more days. How many soldiers left the fort?

Three spraying machines working together can finish painting a house in $60$ minutes. If it take for $5$ machines of the same capacity to do the same job in $x$ minutes, then find the value of $x$.

A group of $3$ friends staying together, consume $54 \mathrm{k}\mathrm{g}$ of wheat every month. Some more friends join this group and they find that the same amount of wheat lasts for $18$ days. How many new members are there in this group now?

$55$ cows can graze a field in $16$ days. How many cows will graze the same field in $10$ days?

$18$ men can reap a field in $35$ days. For reaping the same field in $15$ days, how many men are required?

A person has money to buy $25$ cycles worth $₹ 500$ each. How many cycles he will be able to buy if each cycle is costing $₹ 125$ more?

Raghu has enough money to buy $75$ machines worth $₹ 200$ each. How many machines can he buy if he gets a discount of $₹ 50$ on each machine?

If $x$ and $y$ vary inversely as each other and $x=30$, find  $y$ when constant of variation $=900$.