A piece of cloth costs Rs. 35. If the piece were 4 m longer and each metre costs Re. one less, the cost would remain unchanged. How long is the piece ?

The cost of cultivation of a 30 m long pieces of land is Rs. 150. Had the breadth of the land been 5m. Less, the cost would have been Rs. 120. Let's calculate the breadth of the land.

The length and breadth of a cuboid -shaped piece of wood are 2.3 metres and 0.75 metres respectively. If the volume of the wooden piece be 1.104 cubic-metres, then how may piece of wood of size 2.3m xx 0.75 m xx0.04m can be cut off from this piece of wood ?

A tank with rectangular base and rectangular sides , open at the top is to be constructed so that its depth is 2 m and volume is 8m^(3) . If building of tank costs Rs. 70 per square metre for the base and Rs. 45 per square metre for sides, what is the cost of least expensive tank ?

The numbers 2,3,4,5 and 6 written on five pieces of paper. Theses pieces of paper are put in a bag and then mixed thoroughly. A man draws at random two pieces of paper from the bag one after the other without replacement. Describe the following events associated with this random experiment : A : the number on the first piece is less than the one on the second piece, B: the sum of the numbers on the two pieces is 8 or 9 , C: the number on the first piece is odd and D: the number on the second piece is greater than 4. Is there any pair of events which are mutually exclusive?

(Manufacturing problem): A manufacturing company makes two models A and B of a product. Each piece of Model A requires 9 labours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing the maximum labour hors available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model Aand Rs. 12000 on each piece of Model B. How many piecesof Model A and Model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

A storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m. Find the cost of painting it on the outside at rite of Rs. 20per m^2 .

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m^(3) . If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?