Solve the following:
Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

Two person can finish the work in 7 days. (i) One of the persons fell ill before the work started . How much time will the other person take to finish the same work. (ii) How many persons will be needed to finish the work in one day.

Represent the following situations mathematically: John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

A train time table must be compiled for various days of the week, so that two trains twice a day depart for three days, one train daily for two days, and three trains once a day for two days. How many different time tables can be compiled? a. 140 b. 210 c. 133 d. 72

Form the pair of linear equations In the following problems and find their solutions (if they exist) by any algebraic method. :- Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test ?

Three girls are climbing down a staircase.One girl climbs down two steps at one go.The second girl three steps at one go and the third climbs down four steps.They started together from the beginning of the staircase leaving their foot marks.They all came down in complete steps an had their foot marks together at the bottom of the staircase.In how many steps would there be only one pair of foot mark?

There are two factories located one at place P and the other at place Q. From these locations, a certain commodity is to be delivered to each of the three depots situated at A, B and C. The weekly requirements of the depots are respectively 5,5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost of transportation per unit is given below : How many units should be transported from each factory to each depot in order that the transportable cost is minimum. When will be the minimum transportation cost?