1. Solve the following equations:
(i) (2x + 3) / (x+3) = 3/2
(ii) (3x - 5) / (x + 5) = 1
(iii) (2x — 11) / (5x + 13) = O
(iV) (l+x) / (1-x) :2/3
(V) (3x+5) / (3x+4) = 5
` 2. The sum of two numbers is 80 and their ratio is 3:5. Find the numbers.
3. A number is such that it is as much greater than 84 as it is less than 108. Find it ?
4. A steamer goes downstream and covers a distance between two ports in 4 hrs. While it
covers the same distance upstream in 5hrs. If the speed of the stream is 2km/ hr. Find the
speed of the steamer in still water.
5. The difference of two positive numbers is 69 the quotient obtain on dividing one by the other is 4. Find the number.
6. The difference between two sisters is 10 years if 15 years ago the elder one was twice as old as younger one. Find their present ages.
7. Divide 150 into three parts such that the second number is 5/6 the first and the third number 4/ 5 the second .
8. ln a fraction twice the numerator is 2 more than the denominator. lf 3 is added to the numerator and to the denominator, the new fraction is 2/ 3. Find the original fraction.
9. The length of a rectangle is 8 cm more than its width if the perimeter of the rectangle is 44 cm. Find the length and breadth of the rectangle.
10. A bag contains coins of denomination of 50 paisa and 5 rupees. The total value of these
coins is Rs.300. lf the total numbers of coins in the bag is 150, find the number of coins of each type.
11. The sum of the digits of a two digit number is 10. lf the number formed by reversing the digits is less than the original number by 36, find the number.
12. The length of a rectangular room exceeds its breadth by 4 metre. lf the length is increased by 6 m and breadth is diminished by 4m , there would be no change in the area , find the length and the breadth of the room.
13. Two trains with the speed of 35km/ hr and 28 km/ hr respectively, starting at the same time, run in the opposite direction between two stations A and B 315 km apart. Find when and where they will meet.
14. A man leaves half his property to his wife, 1/3 to his son and the remaining to his daughter. lf the daughter’s share is Rs 15000, how much money did the man leave? How much money did his wife get and what is his son’s share?
15. One third of which number must be subtracted from 7/ 11 to give 24/ 55?
16. If the same number is added to both the numerator and the denominator of a fraction 3/ 5, then the result is 3/4. Find the number.
17. Two numbers are such that the ratio between them is 5:7. If 7 is added to each of them , the ratio becomes 3:4. Find the numbers. .
18. 2/ 3 of a number is 20 less than the original number. Find the number.
19. lf 10 is added to four times a certain number, the result is 5 less than 5 times the number. Find the number. I
20. The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and denominator decreased by 6, the new becomes 2. Find the original number.
21. The angle A of a triangle ABC is equal to the sum of the other two angles Also the ratio of the measure of angle B to that of C is 4: 5. Find the three angles.
(4) Let the speed of the streamer in still water be x km/hr.
Speed of the stream = 2 km/hr
Let the distance between the posts be d km.
Downstream speed = (x + 2) km/hr.
Upstream speed = (x – 2) km/hr
Time taken to cover – Downstream distance = 4 hrs
Time taken to cover upstream distance = 5 hrs
Let money left by the man is Rs x.
Money left by the man = Rs 90000
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