O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 2: Exercise

Divide $36$ into four parts so that if $2$ is added to the first part, $2$ is subtracted from the second part, the third part is multiplied by $2$, and the 
fourth part is divided by $2$, then the resulting number is the same in each case. 
 

There were $2500$ persons who bought tickets to see a village fair. The adults paid $75$ paise each for their admission tickets but the children paid $25$ paise each. If the total receipts amounted to $₹1503$, using an equation method, find how many children saw the fair?

In a triangle, the sum of the two angles is equal to the third. If the difference between them is $50°$, determine the angles.

In a parallelogram, one angle is ${\left(\frac{2}{5}\right)}^{\mathrm{th}}$ of the adjacent angle. Determine the angles of this parallelogram.

The boat goes $24 \mathrm{km}$ upstream and $28 \mathrm{km}$ downstream in $6$ hours. It goes $30 \mathrm{km}$ upstream and $21 \mathrm{km}$ downstream, in $6\frac{1}{2}$ hours. Find the speed of the boat in still water and also the speed of the stream.

Satish and Ashok start at the same time from two places $21 \mathrm{km}$ apart. If they walk in the same direction Satish overtakes Ashok in the $21$ hours but if they walk in opposite directions, they meet in $3$ hours. Find the rate at which each of them walks.

A boy walks to a picnic spot from his house in $6$ hours, but he can travel the same distance on his cycle in $2$ hours. If his average cycling speed is $7$ kilometres per hour faster than his average walking speed, find his average walking speed and his average cycling speed. 

A man travels $600 \mathrm{km}$ partly by train and partly by car. If he covers $400 \mathrm{km}$ by train and the rest by car, it takes him $6$ hours and $30$ minutes. But if he travels $200 \mathrm{km}$ by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.