Linear Equations in two variables-Important Questions

1.  6 men and 10 women can finish making pots in 8 days, while the 4 men and 6 women can finish it in 12 days. Find the time taken by the one man alone from that of one woman alone to finish the work.
2.  A boat covers 14 kms in upstream and 20 kms downstream in 7 hours. Also it covers 22 kms upstream and 34 kms downstream in 10 hours. Find the speed of the boat in still water and of that the stream.
3.  Draw the graph of 2x+y=6 and 2x-y+2=0. Shade the region bounded by these lines and x axis. Find the area of the shaded region
4.  When you add two numbers and the number obtained by reversing the order of its digits is 165. If the both numbers differ by three, find the number.
5.  A number say z is exactly the four times the sum of its digits and twice the product of the digits. Find the numbers.
6.  Solve graphically 4x-3y+4=0, 4x+3y-20=0
7.  There are two points on a highway a,b. They are 70 km apart. An auto starts from A and another auto starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other they meet in 1 hour. Find how fast the two autos are.
8.  A diver rowing at the rate of 5 km/h in still water takes double the time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
9.  The larger of two supplementary angles exceeds thrice the smaller by 20 degrees. Find them.
10.  The sum of two children is ‘a’. The age of the father is twice the ‘a’. After twenty years, his age will be equal to the addition of the ages of his children. Find the age of father.