R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 1B

Find the largest four-digits number which when divided by $4, 7$ and $13$ leaves a remainder of $3$ in each case.

Find the least number which should be added to $2497$ so that the sum is exactly divisible by $5, 6, 4$ and $3$.

Find the greatest number that will divide $43, 91$ and $183$ so as to leave the same remainder in each case.

Find the least number which when divided by $20, 25, 35$ and $40$ leaves remainders $14, 19, 29$ and $34$ respectively.

Find the maximum number of students among whom $1001$ pens and $910$ pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils.

Find the least number of square tiles required to pave the ceiling of a room $15 \mathrm{m} 17 \mathrm{cm}$ long and $9 \mathrm{m} 2 \mathrm{cm}$ broad.

Three measuring rods are $64 \mathrm{cm}, 80 \mathrm{cm}$ and $96 \mathrm{cm}$ in length. Find the least length of cloth that can be measured an exact number of times, using any of the rods.

The traffic lights at three different road crossings change after every $48$ seconds, $72$ seconds and $108$ seconds respectively. If they all change simultaneously at $8 \mathrm{a}.\mathrm{m}$. then at what time will they again change simultaneously?