31.

The following distribution gives the daily income of 50 workers of a factory:

Daily Income (In)	100-120	120-140	140-160	160-180	180-200
Number of workers	12	14	8	6	10

Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

A motor boat whose speed is 18 km/hr in still water 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed.  It takes 3 hours to complete the total journey, what is the original average speed ?

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC 60. Then construct a triangle whose sides are 3/4 of the corresponding sides of the △ABC.

In an equilateral △ABC, is a point on side BC such that BD =1/3BC. Prove that 9 (AD)² = 7(AB)²

Prove that, in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.