Proportion, Direct Inverse and Joint Variation with Solved Examples

In the previous video some part of the video became blurred in which I told you how compare 2 to 4 ratios and find out the overall ratio between them. That part I have again covered in this video. After finishing that I have started with the explanation of Proportion Part of Ratio and Proportion. I have explained the terms Mean Proportional and Continued Proportion. I have also explained variation. Variation is basically of three types - Direct Variation, In-direct Variation and Joint Variation. Then I have started with question solving. I will again remind you that please look at the question solving part with full concentration as through this I have revised all the concepts and have also told many short tricks that I have not discussed while teaching you the theory part.

Questions discussed in this video are listed below - 

Question 1. One year ago, the ratio between Ram and Shyam salaries was 3:5. The ratios of their individual salaries of last year and present year are 2:3 and 4:5 respectively. If their total salaries for the present year is Rs. 86000, find the present salary of Ram.

Question 2. The number 225 is divided into four parts p,q,r and s such that p = 2q = 3r= 4s. What is the value of p+q ?

Question 3. Rs. 74000 is distributed among a, b and c in the ratio 1/4:1/5:1/6. The share of b is

Question 4. Given that a,b and c are non-zero real numbers and a/2 = b/3 = c/4 = (2a - 3b + 5c)/k  . Find the value of k

Question 5. A person has a total of Rs. 210 in one-rupee, 50 paise and 25 paise coins. The number of the three type of coins are in the ratio 2.5:3:4 respectively. How many one-rupee coins has the person got ?

Question 6. A sum of money is divided among A,B and C such that for each Rs. 2, A gets Rs. 1, B gets 65 paise and C gets 35 paise. If C's share is Rs. 560, find the original sum ??

Question 7. The income of X and Y are in the ratio 4:3 and their expenditures are in the ratio 2:1 . If each one saves Rs. 1000, find their respective incomes.

Question 8. A man ordered four pair of black socks and some pair of brown socks. The price of a black pair is double that of a brown pair. While preparing the bill, the clerk interchanged the numbers of black and brown pairs by mistake which increased the bill by 50 %. What was the ratio of the number of black and brown pair of socks in the original order ?

Question 9. Monthly income of A and B are in the ratio 1:3 and their expenses are in the ratio 19:40. A saves Rs. 18860 less than B and in total they save Rs. 36020. What are their respective incomes ?

Question 10. A student scored marks in the ratio 5:4:6:8:7 in five subjects having equal maximum marks. He scored 50 % of the maximum marks in all the five subjects taken together. In how many subjects did he score more than 55 % of the maximum marks ?

Question 11. The height of Santosh is proportional to the square root of his age. What will be the height of Santosh at 16 years, if he is 4 feet tall at the age of 9 years ?

Question 12. The pressure of a gas is directly proportional to its temperature and inversely proportional to its volume. The initial pressure, volume and temperature are 150 pascals, 20 cubic meter and 100 degree kelvin respectively. Find the temperature if the final volume and pressure of the same gas are 8 cubic meter and 150 pascals respectively under same conditions.

Question 13. B is the sum of three quantities which are directly proportional to A, A², A³ respectively, and when A = 1, Y = 4, when A = 2, Y = 8 and when X = 3, Y = 18. What is the value of Y when X = 7 ?

Question 14. The total cost of a trip is constant. The cost per head reduces from Rs. 25 to Rs. 20, when 20 more people join in. Find out how much it would reduce further if 25 people more join this new group ??