Ratio and Proportion STD V and VI

Ratio and Proportion

1.      A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
     Answer:

     4A/15 = 2B/5 = k, say
     or, A = 15k/4, B = 5k/2 
     therefore, 15k/4 + 5k/2 = 1210 
     or, k = 1210 x 4/25 
     so, B has = 5k/2 =  1210 x 4 /25 x (5/2) = 484

2.      A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

     Answer:
     let the total amount be T
    
     Share of C = (4/14) x T 
     Share of D = (3/14)  x T

    Given (4/14)T - (3/14)T = 1000
     or, T = 14000
     or, B = (2/14) x 14000 = 2000

3.      In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quantity of water to be further added is ..................
    
     Answer:
     M/W = 2/1
     so, milk = (2/3) x 60 = 40 litres and water = 20 litres
      
     now, 40/ W = 1/2 or, W = 80
     So, additional  water to be added is 80 - 20 = 60 litres

4.      The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

      Answer:

      Total strength of class = T
      Boys = (7/15)T, Girls = (8/15)T
      New number of boys = 1.2 x (7/15)T = (8.4/15)T, New number of girls = 1.1 x (8/15)T = 8.8T/15
      B/G = 8.4/8.8 = 84/88 = 21/22

5.      Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

      Answer:

      R/S = 2/3
      or, R/2 = S/3 = k say, So, R = 2k and S = 3k
      Now, (2k + 4000)/(3k + 4000) = 40/57
      or, 114k + 4000 x 57 = 120k + 40 x 4000
      or, 6k = 4000 x ( 17)
      or, 3k = S = 2000 x 17 = 34000
      present salary of Sumit = 34000 + 4000 = 38000/-

6.      The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is ...............

      Answer:

      A/B = 2/3, and B/C = 5/8
      or, A/B = 10/15 and B/C = 15/24
      or, A: B:C = 10:15:24
      So, the second number is 98 x { 15/ (10+15+ 24)  } = 30

7.      If Rs. 782 be divided into three parts, proportional to: 1/2 , 2/3, 3/4 , then the first part is ................................

      Answer: A:B:C = 1/2 : 2/3 : 3/4 
      Multiplying with factor after taking LCM of denominator ( 12)
      A:B:C = 6 : 8 : 9

      So, the first part is = 782 x {6 / ( 6 + 8  + 9) = 204
 

8.      The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries

      Answer:
      let the Total  salary be T
      New Salary of A = 1.15 x 2T/10 = 2.30T/10
     
New Salary of B = 1.10 x 3T/10 = 3.3T/10
     
New Salary of C = 1.20 x 5T/10 = 6T/10

      new ratio = 2.3: 3.3 : 6 = 23: 33 : 60

9.      If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

      Answer: 

       4A/10 = 2B/3

       or A/B = 10 x 2 / (3 x 4) = 5/3

10.   Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is ..................................

      Answer:

       A/B = 3/5 or, A/3 = B/5 = k say
    
       So, A = 3k and B = 5k
 
       (3k - 9)/ (5k - 9) = 12: 23

       or, 69k - 9x 23 = 60k - 9 x 12

       or, 9k = 9 x 9

       or, k = 9

       So, the smaller number is = 3k = 3 x 9 = 27.