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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

13. Two whole numbers whose sum is 72 cannot be in the ratio?

• A. 3 : 4
• B. 3 : 5
• C. 4 : 5
• D. 5 : 7
 Ans: A. Sol. The sum of the ratio terms must divide 72. So, the ratio cannot be 3 : 4.

14. The price of a scooter and a T.V. are in the ratio 7 : 5. If the scooter costs Rs. 8000 more than a T.V. set, then the price of a T.V. set is

• A. Rs. 20,000
• B. Rs. 24,000
• C. Rs. 28,000
• D. Rs. 32,000
 Ans: C. Sol. Let the prices of a scooter and T.V. set be Rs. 7x and Rs. 5x respectively. Then, 7x - 5x = 8000 ⇔ 2x = 8000 ⇔ x = 4000. ∴ Price of a T.V. set = Rs. (7 x 4000) = Rs. 28000.

15. 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 =[76x3/19] = 12.