Unit- 12 (Equations)-X

Unit- 12 (Equations)-X

Exercise with Answers:

1. The sum of two numbers is 29 and their difference is 5. Find the numbers. (17, 12)
2. The sum of two angles of a triangle is 105° and their difference is 15°. Find the angles. (60°, 45°)
3. A number is thrice the other. If their difference is 18, find the numbers. (9, 27)
4. The perimeter of a rectangular field is 150m. If the length of the field is 5m. longer than its breadth, find the area of the field. (1400 square meter) 
5. The length of a rectangular pond is 15m. less than twice of its width. If the perimeter of the pond is 330m., find its area. (6300 square meter)
6. The perimeter of a rectangular piece of a land is 140m. The size of the land is decreased due to the expansion of the road and the new length and breadth of the land are equal to times of the original length and breadth respectively. If the new perimeter of the land is 120m, find the original length and breadth of the land. (length = 40m, breadth = 30m)
7. The total cost of 2 tables and 3 chairs is Rs. 5100. If the chair is cheaper than table by Rs. 800, find the cost of their unit items. (Rs. 1500, Rs. 700)
8. The total cost of 3kg apples and 5 kg. oranges is Rs. 1080. If the cost of 3 kg. apples is the same as the cost of 7kg. oranges, find the cost of each kg. of both fruits.(Rs. 210, Rs. 90) 
9. A pair of trousers of a school uniform is more expensive than a shirt by Rs. 300. If the total cost of the trousers and the shirt is Rs. 1200, find the cost of each.(Rs. 700, Rs. 400)
10. Two years ago, the father's age was nine times his son's age. But three years later, the father's age will be five times his son's age only. Find their present ages. (47 years, 7 years)
11. Three years ago, the ratio of the ages of two boys was 4:3. Three years hence, the ratio of their ages will be 11:9. Find their present ages. (19 years, 15 years)
12. Two years ago the age of mother was six times as old as her son. Three years hence, she will be 11 years older than 2 times the age of her son. Find their present ages. (26 years, 6 years)
13. The sum of the digits of a two digit number is 9. If 27 is subtracted from the number, the digits are reversed. Find the number.(63)
14. The sum of the digits of a two digit number is 11. The number formed by interchanging the digits of that number will be 45 more than the original number. Find the number. (38)
15. A number of two digit is 3 more than 6 times the sum of the digits. If the digits are interchanged, the number is decreased by 18. Find the number. (75)
16. The denominator of a fraction is 2 more than its numerator. If 9 is added to the numerator and 3 is subtracted from the denominator, it becomes 2. Find the original fraction. (11/13)
17. If 1 is added to the denominator of a fraction, the fraction becomes ½. If 1 is added to the numerator of the fraction, the fraction becomes 1. Find the original fraction. (2/3)
18. If the numerator of a fraction is multiplied by 6 and the denominator is reduced y 3, the result becomes 6. If the numerator of the fraction is increased by 12 and 3 is subtracted from the thrice of the denominator, the result becomes 8/9. Find the original fraction. (4/7)
19. A bus started its journey from Birgunj to Biratnagar at 6 am. with a uniform speed of 50km/hr. After 1 hour, another bus also started its journey from Birgunj to the same destination with a uniform speed of 60km/hr. At what time would they meet each other? (12:00 noon)
20. Two runners start from the same point at the same time. They will be 8km. apart at the end of two hours if running in the same direction and they will be 26km. apart at the end of one hour if running in opposite direction. Find their speed. (15km/hr, 11km/hr)

Additional Questions and Answers:

21. 7 pens and 5 pencils cost Rs. 375. Again 4 pens and 7 pencil cost Rs. 264. Find the unit price for each pen and pencil. (Rs. 45 and Rs. 12)
22. 6 years ago, a man's age was six times the age of his daughter. After 4 years, thrice his age will be equal to eight times of his daughter's age. What are their present ages? Find it. (36 years and 11 years)
23. The sum of the digits of a two -digit number is 13. If 27 is added to the number, the places of the digits are reversed. Find the number. (58)
24. A bus started its Journey from Kathmandu to Nepalgunj at 3pm. with a uniform speed of 40 km/hr. After 1 hour, another bus also started its Journey from Kathmandu to the same destination with a uniform speed of 50km/hr. At what time would they meet each other? Find it. (8 PM.)