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RATIO AND PROPORTION

RATIO AND PROPORTION

RATIO:

The number of times one quantity contains another quantity of the same kind is called the ratio of the two quantities. (a:b)

PROPORTION:

The equality of ratios is called proportions.
Example: Consider the two ratios

    1st ratio        2nd ratio
5:15           7:21

Direct Proportion:

If the given two quantities are so related to each other that if one of them is multiplied (or divided) by any number, the other is also multiplied (or divided) by the same number.

Inverse Proportion:

    If two quantities are so related that if one of them is multiplied by any number, the other is divided by the same number.

Compound proportion

  1. 30 men repair a road in 56 days by working 6 hours daily. In how many days 45 men will repair the same road by working 7 hours?
  2. If 60 women spin 48kg of cotton by working 8 hours daily, how much cotton will 30 women spin by working 12 hours daily?
  3. If the price of a carpet 8 meter long & 3 meter wide is Rs. 6288, what will be the price of 12 meter long and 6 meter wide?
  4. If 15 labourers earn Rs. 67500 in 9 days, how much money will 10 labourers earn in 12 days?
  5. 70 men can complete a wall of 150 meter length in 12 days. How many men can complete the wall of length 600 meter in 30 days?
  6. If the fare of 12 quintal luggage for a distance of 18 km is 12 rupees. How much fare will be charged for a luggage of 9 quintals for a distance of 20 km?
  7. 14 masons can build a wall 12 meter high in 12 days. How many masons will be needed to build a wall 120 meter high in 7 days?
  8. 15 machines prepare 360 sweaters in 6 days. 3 machines get out of order. How many sweaters can be prepared in 10 days by the remaining machines?
  9. 1440 men had sufficient food for 32 days in a camp. How many men may leave the camp so that the same food is sufficient for 40 days when the ratio is increased by 1½ times (the first element is 1 and the second is 3/2)
  10. Ten men can assemble 400 cycles in 8 days. How many cycles 5 men will assemble if they work for 16 days?
  11. Mr Khan, Mr Furqan and Mr Toseef are three partners. They earned a profit of Rs. 18000. The profit can be shared in the ratio A:B=2:5 and B:C=10:4. Find share of each partner.

Answers

1. 32 days    2. 36 kg        3. Rs. 18864
4. Rs. 60,000    5. 112 men    6. Rs. 10
7. 240 masons    8. 480 sweaters    9. 672 men
10. 400 cycles     11. A = 4000    B = 10,000
C = 4000

MCQs

1. If 3 men and 6 boys can do a piece of work in 20 days, how many days 6 men and 8 boys will take?

(a) 6 days    (b) 8 days
(c) 9 days     (d) 20 days

2. If 20 men can do a piece of work in 8 days, how many men will finish it in 10 days?
(a) 4 men    (b) 16 men
(c) 8 men    (d) 18 men

3. Pipe “A” can fill a tank in 5 minutes when “B” can fill it in 6 minutes. How long it would take both pipes, working together, to fill it?
(a) 19/3 min    (b) 11/3 min
(c) 30/11 min    (d) 29/4 min

4. A and B together have Rs. 1210. If 4/15 of A’s amount is equal to 5/2 of B’s amount, how much amount does B have?
(a) Rs. 460    (b) Rs. 484
(c) Rs. 550    (d) Rs. 664

5. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
(a) 2:5        (b) 3:5
(c) 4:5            (d) 6:7

6. A sum of money is to be distributed among A, B, C and D in the proportion of 5:2:3. If C gets Rs. 1000 more than D, what is B’s share?
(a) Rs. 500       (b) Rs. 1500
(c) Rs. 2000       (d) Rs. 2500

7. Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
(a) 2:3:4       (b) 6:7:8
(c) 6:8:9       (d) None of these

9. In a mixture 60 litres, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is:
(a) 20 litres      (b) 30 litres
(c) 40 litres      (d) 60 litres

10. Salaries of Ali and Aslam are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Aslam’s salary?
(a) Rs. 17,000   (b) Rs. 20,000
(c) Rs. 25,500   (d) Rs. 38,000

11. 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:
(a) 20            (b) 30
(c) 48            (d) 58

12. The salaries of 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 the new ratio of their salaries?
(a) 3:3:10       (b) 10:11:20
(c) 23:33:60     (d) None of these

13. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second one?
(a) 2:5            (b) 3 :7
(c) 5 :3            (d) 7:3

14. The fourth proportional to 5, 8, 15 is:
(a) 18            (b) 24
(c) 19            (d) 20

15. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1:2:3. If there is Rs. 30 in all, how many 5 p coins are there?
(a) 50           (b) 100
(c) 150        (d) 200

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