triangles / ratio and proportions

The Ratio of altitudes of a triangle are 1:2:3. Find the ratio of its side.

ratio and proportion

The ratio of marks obtained by Nanu and Bhanu is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted. 

ratio and proportion

Two alloys A and B are composed of two basic elements p and q. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X?

ratio and proportion, ipm, mtse

A house has dogs, cats and parrot in the ratio of 3:7:5. If the number of cats was more than the number of dogs by a multiple of both 9 and 7 then what is the minimum of pets in the house possible?

ratio and proportion

ratio and proportion

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.

MTSE STD V ratio proportion question and answer

The sum of ages of the son and mother is in the ratio of 2: 14. When the son was born the mother was 24 years old. What is the age of mother and son?

MTSE STD V

Answer:

Ratio and Proportion

 

Ratio and proportion

Show that:

If,

                 ax+cy+bz=0 ---- (1)
                 cx+by+az=0 ---- (2)
                 bx+ay+cz=0 ---- (3)

Then, a³+b³+c³ = 3abc
 

Ratio and Proportion

Find the ratio x:y:z from the following set of equation:

ax+by+cz=0
lx+my+nz=0

ratio and proportion

solution of problems in algebra from Hall

ratio and proportion

solution to problems in algebra from Hall

Ratio and Proportion

Solution to Problems in Algebra from Hall

Ratio and Proportion

Solution of problems in algebra from Hall

ratio and Proportion

solution to problems in Algebra from Hall

ratio and proportion

Solution to problems in Algebra from Hall

Ratio and Proportion

Solution to problems in algebra from Hall

Ratio and Proportion

Solution to problems in Algebra from Hall

ratio and Proportion

Solution of Problems in algebra from from Hall