# NCERT Mathematics Class 10 Exemplar Ch 3 Pair of Linear Equations in Two Variables Part 6

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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.

Answer: 40 years.

18. Two numbers are in the ratio . If 8 is subtracted from each of the numbers, the ratio becomes . Find the numbers.

Answer: 40, 48.

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 B. 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.

Answer: 100 students in hall A, 80 students in hall B.

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. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

Answer: Rs 10, Rs 3.

21. In a competitive examination, one mark is awarded for each correct answer while 1 2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Answer: 100.

22. The angles of a cyclic quadrilateral ABCD are Find x and y, and hence the values of the four angles.

Answer: , , , ,