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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

4. A ratio between two numbers is 3 : 4 and their L.C.M. is 180. The first number is

• A. 60
• B. 45
• C. 20
• D. 15
 Ans: B. Sol. Let the required numbers be 3x and 4x. Then, their L.C.M. is 12x. ∴ 12x = 180⇔ x = 15. Hence, the first number is 45.

5. The compounded ratio of (2:3), (6:11) and (11:2) is

• A. 2 : 1
• B. 1 : 2
• C. 36 : 121
• D. 11 : 24
 Ans: A. Sol. Required ratio = [2/3 x 6/11 x 11/2] = 2/1 = 2 : 1.

6. If 0.75 : x : : 5 : 8, then x is equal to

• A. 1.12
• B. 1.25
• C. 1.20
• D. 1.30
 Ans: C. Sol. (x×5) = (0.75×8) ⇒ x = 6/5 = 1.20.