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We observe that the lines represented by i and ii are coincident. Write the vertices of the triangle formed by these lines and the y-axis. Also, find the area of this triangle? How many such lines can we find?
Therefore, the pair of equations has a unique solution. Hence, these equations are consistent. Find x and y. Question 16 Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now? Now, by first condition, Two years ago, Salim was thrice as old as his daughter. Question 17 The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children.
Find the age of the father. Solution: Let the present age in year of father and his two children be x, y and z years, respectively. Question 18 Two number are in the ratio 5 : 6, If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers. Solution: Let the two numbers be x and y. Question 19 There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to 8.
But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls. Solution: Let the number of students in halls A and B are x and y respectively. Question 20 A shopkeeper gives books on rent for reading.
She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Find the fixed charges and the charge for each extra day. Jayanti answered questions and got 90 marks. How many questions did she answer correctly? Solution: Let the number of correct answers be x then the number of wrong answers be � x Then, by given condition, Hence, Jayanti answered correctly questions.
Find x and y and hence the values of the four angles. Also find the area of the quadrilateral formed by the lines and the x-axis. Now, from the graph ABCD is the quadrilateral formed by given lines and x � axis. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box. On solving lines i and ii , we will get the intersecting point B On multiplying eq. On solving lines iii and i , we will get the intersecting point A On multiplying in eq.
Question 6 Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour, if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus. Now, time taken to travel 2 km by rickshaw, and time taken to travel remaining distance i. Find the speed of the stream.
Question 8 A motorboat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream. Question 9 A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number. Question 10 A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket.
One reserved first class ticket from the stations. Situations worsen if they are not prepared for it fully. It prepares students for the Board exams. These books serve as a self-explanatory guidebook having questions of varied difficulties. In fact, the books will help them to solve the questions in many other ways. The book serves as a self-assessment for students. In fact, students can solve the questions and rectify their mistakes easily.
The chapters are explained in a proper manner, with equations and formulae wherever required. They are a very good resource for preparing the students to face critical questions. Firstly, it has various types of questions, depending on difficulty levels. Secondly, the conceptual sums will increase the logical and analytical power of the students.
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