RATIO AND PROPORTION

1.If a:b=3:7,find the value of (5a+b):(4a+5b)

  a)15:44      b)22:35 c)15:49 d)22:47

2.The ratio between two number is 3:5 and their is 40.Find the larger of two numbers

  a)15  b)20    c)25    d)40

3.A bag contains one rupee,50 paise and 25 paise coins in the ratio 1:2:4.If the

  total amount is Rs 75,then find the number of 50 paise coins in the bag

  a)25  b)50    c)75    d)100

4.If (x+4):(3x+15) is the triplicate of 2:3.Find the value of x

  a)1   b)3     c)4     d)none of these

5.If a is 75% of b,b is 150% of c and d is 25% of c,then find a:d

  a)9:1 b)9:2   c)8:3   d)8:1

6.The present ages of two persons are in the ratio 7:8.Twenty years ago the ratio of

  their ages was 9:11.Find the present age of the older son

  a)64 years   b)72 years     c)56 years     d)40 years

7.Find x:y:z,if 2x+y-5z = 0 and 3x-2y-4z=0

  a)1:2:1      b)1:1:1 c)1:1:2 d)2:1:1

8.A certain sum is divided among A,B and C in a manner that for every rupee that A 

  gets,B gets 75 paise and for every rupee that B gets,C gets 50 paisee.If B's share

  in the total sum is Rs 840.Find the share of A

  a)Rs 2380    b)Rs 2240      c)Rs 1750      d)Rs 1120

9.Seventy eight is divided into two parts such that five times the first part and four

  times the second part are in the ratio 15:14.Find the first part

  a)32  b)36    c)42    d)46

10.A certain amount of money  is divided among A,B and C such that A gets half of what

   B and C gets together.B gets one third of what A and C together get.If A got Rs 500 

   more than B,then how much money was divided?

  a)Rs4500     b)Rs 6000      c)Rs 8000      d)none of these

11.In a school there are 650 students.The ratio of the boys to that of the girls is 8:5.

   How many more girls should join the school so that the ratio becomes 4:3?

  a)25  b)50    c)100   d)200

12.A variable x varies directly as the cube of another variable y.if x=4,y=2,then find y

   when x = 32

  a)4   b)8     c)16    d)32

13.What should be subracted from both the numbers which are in the ratio 3:4 so that the

   ratio becomes 2:3

  a)4   b)6     c)10    d)cannot be determined

14.A varies directly as the sum of the quantities B and C.B in turn varies directly as x and 

   C varies inversely as x.When x=2,A = 6 and when x=4,A=9.Find the value of A when the value 

   of x=16

  a)2 1/2      b)1     c)8 1/2 d)32 1/4

15.The volume of a shere varies directly as the cube of its radius.If three cubes of radii 3 

   cm,4 cm and 5 cm are melted and recast into one sphere,then find the radius of the sphere

  a)5.5 cm     b)6 cm  c)7 cm  d)7.5 cm

Directions for question 16 to 18:These questions are based on the data given below

   There are two colleges in the town-college A and college B.There are 500 students more in

 college A than in college B.The ratio of the boys to that of the girls in college A is 3:2 

 and that in college B is 4:1.The ratios of the number of science,humanities and commerce 

 students in college A and college B are respectively 2:5:3 and 2:3:3.The number of commerce

 students in both the colleges is the same.

16.How many students are there in college A?

   a)2000      b)2500  c)3000  d)3500

17.How many girls are there in two colleges together?

   a)1400      b)1600  c)1700  d)2000

18.How many more/less humanities students are there in college A than in college B?

   a)400 more  b)400 less     c)500 less     d)500 more

19.If (2x+5):(7x-6) is the duplicate ratio of 5:8,then find the value of x

   a)6  b)7     c)10    d)none of these

20.The mean proportional between two numbers is 16 and their third proportional is 128.Find the

   smaller of the two numbers

   a)8  b)12    c)16    d)32

21.A bag contains 50 p,25 p and 10 p coins in the ratio 5:9:4,amounting to Rs 206.Find the 

   number of coins of each type

   a)200,360,160       b)160,360,200  c)360,373,123  d)678,234,763

22.what is the ratio whose terms differ by 40 and the measure of which is 2/7?

   a)16:56     b)14:56 c)15:56 d)16:72

23.A sum of Rs 53 is divided among A,B,C in such a way that A gets Rs 7 more than what B gets

   and B gets Rs 8 more than what C gets.The ratio of their shares is

   a)16:9:18   b)25:18:10     c)18:25:10     d)15:8:30

24.A certain amount was divided between A and B in the ratio 4:3.If B's share was Rs 4800,the 

   total amount was

   a)Rs 11,200 b)Rs 6,400     c)Rs 19,200    d)Rs 39,200

25.If 10% of x = 20% of y,then x:y is equal to

   a)1:2       b)2:1   c)5:1   d)10:1

26.x varies inversely as square of y.Given that y=2 for x=1.The value of x for y=6 will be 

   equal to

   a)3  b)9     c)1/3   d)1/9

27.The ratio of incomes of A and B is 5:4 and the ratio of their expenditures is 3:2.If at

   the end of the year,each saves Rs 1600,then income of A is

   a)Rs 3400   b)Rs 3600      c)Rs 4000      d)Rs 4400

28.Three containers have their volumes in the ratio 3:4:5.They are full of mixtures of milk  

   and water.The mixtures contain milk and water in the ratio of (4:1),(3:1) and (5:2) resp.

   The contents of all these three containers are poured into a fourth container.The ratio

   of milk and water in the fourth container is

   a)4:1       b)151:48       c)157:53       d)5:2

29.In a school,10% of the boys are same in number as 1/4rth of the girls.What is the ratio of

   boys to girls in that school?

   a)3:2       b)5:2   c)2:1   d)4:3

30.The ratio of number of boys and girls in a school is 3:2.If 20% of the boys and 25% of the

   girls are scholarship holders,what percentage of the students does not get the scholarship?

   a)56 b)70    c)78    d)80

31.The sides of a triangle are in the ratio 1/2:1/3:1/4 and its perimeter is 104 cm.The length 

   of the longest side is

   a)52 cm     b)48 cm c)32cm  d)26cm

32.which of the following ratios is greatest?

   a)7:15      b)15:23 c)17:25 d)21:29

33.In a college the ratio of number of girls to boys is 8:5.If there are 160 girls,the total 

   number of students in the college is

   a)100       b)250   c)260   d)416

34.The least whole number which when subracted from both the terms of the ratio 6:7 gives

   a ratio less than 16:21 is

   a)2  b)3     c)4     d)6

35.The speeds of three cars are in the ratio 5:4:6.The ratio between the time taken by them

   to travel the same distance is

   a)5:4:6     b)6:4:5 c)10:12:15     d)12:15:10

36.15 litres of mixture contains 20% alcohol and the rest water.If 3 litres of water be mixed

   with it,the percentage of alcohol in the new mixture would be

   a)15 b)16 2/3       c)17    d)none of these

37.20 litres of mixture contains milk and water in the ratio 5:3.If 4 litres of this mixture 

   be replaced by 4 litres of milk,the ratio of milk to water in the new mixture would be

   a)2:1       b)7:3   c)8:3   d)4:3

38.85 kg of a mixture contains milk and water in the ratio 27:7.How much more water is to be

   added to get a new mixture containing milk and water in the ratio 3:1?

   a)5kg       b)6.5kg c)7.25kg       d)8kg

39.The ages of A and B are in the ratio 3:1.Fifteen years hence,the ratio will be 2:1.Their

   present ages are

   a)30,10     b)45,15 c)21,7  d)60,20

40.The average age of three boys is 25 years and their ages are in the proportion 3:5:7.The 

   age of the youngest boy is

   a)21 b)18    c)15    d)9