R. D. Sharma Solutions for Chapter: Playing With Numbers, Exercise 8: EXERCISE

What is the largest number that divides $626,3127$and $15628$and leaves remainders of $1, 2$ and $3$ respectively$?$

The length, breadth and height of a room are $8 \mathrm{m} 25 \mathrm{cm}, 6 \mathrm{m} 75 \mathrm{cm}$ and $4 \mathrm{m} 50 \mathrm{cm}$ respectively. Determine the longest rod which can measure the three dimensions of the room exactly.

A rectangular courtyard is $20 \mathrm{m} 16 \mathrm{cm}$ long and $15 \mathrm{m} 60 \mathrm{cm}$ broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

Determine the longest tape which can be used to measure exactly the lengths $7 \mathrm{m}, 3 \mathrm{m} 85 \mathrm{cm}$ and $12 \mathrm{m} 95 \mathrm{cm}$.

$105$ goats, $140$ donkeys and $175$ cows have to be taken across a river. There is only one boat which will have to make many trips in order to do so. The lazy boatman has his own conditions for transporting them. He insists that he will take the same number of animals in every trip and they have to be of the same kind. He will naturally like to take the largest possible number each time. Can you tell how many animals went in each trip.

Reduce each of the following fractions to the Iowest terms :

$\frac{161}{207}$

Reduce each of the following fractions to the Iowest terms :

$\frac{296}{481}$

A merchant has $120 \mathrm{litres}$ of oil of one kind, $180 \mathrm{litres}$ of another kind and$240 \mathrm{litres}$ of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin$?$