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## Ratio and Proportion -> IMPORTANT FACTS AND FORMULAE

 Ratio : The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a : b. Proportion : The equality of two ratios is called proportion. Mean Proportional : Mean Proportional between a and b is √ab. Fourth Proportional : If a : b = c : d, then d is called the fourth proportional to a,b,c. Third Proportional : If a : b = b : c, then c is called the third proportional to a and b. Duplicate ratio : of (a : b) is (a2 : b2). Sub-duplicate ratio : of (a : b) is (√a : √b). Triplicate ratio : of (a : b) is (a3 : b3). Variation : (I). We say that x is directly proportional to y, if x = ky for some constant k and we write, x∝y. (II). We say that x is inversely proportional to y, if xy = k for some constant k and we write, x∝1/y.

## Ratio and Proportion -> SOLVED EXAMPLES

1. Divide Rs. 1162 among A, B, C in the ratio 35 : 28 : 20. Sol. Sum of ratio terms = (35 + 28 + 20) = 83. A's share = Rs.[1162 x 35/83] = Rs. 490. B's share = Rs.[1162 x 28/83] = Rs. 392. C's share = Rs.[1162 x 20/83] = Rs. 280. If a : b = 5 : 9 and b : c = 4 : 7, find a : b : c. Sol.a : b = 5 : 9 and b : c = 4 : 7 = (4x9/4) : (7x9/4) = 9 : 63/4 ⇒ a : b : c = 5 : 9 : 63/4 = 20 : 36 : 63.

## Ratio and Proportion -> EXERCISE

19. If 76 is divided into four parts proportional to 7,5,3,4 then the smallest part is

• A. 12
• B. 15
• C. 16
• D. 19
 Ans: A. Sol. Given ratio = 7 : 5 : 3 : 4, sum of ratio terms = 19. ∴ Smallest part = (76 x 3/19) = 12.

20. If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is

• A. 2 : 3
• B. 3 : 4
• C. 3 : 20
• D. 20 : 3
 Ans: C. Sol. 0.4A = 0.06 B ⇔ A / B = 0.06 / 0.40 = 6/40 = 3/20. ∴ A : B = 3 : 20.

21. 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. 9 years
• B. 15 years
• C. 18 years
• D. 21 years
 Ans: B. Sol. Total age of 3 boys = (25 x 3) years = 75 years. Ratio of their ages = 3 : 5 : 7. Age of the youngest = (75 x 3/15)years = 15 years.