## FeedBack Form

Your Name : : : :
FeedBack

## 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

22. Salaries of Prasanna and Sathish are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sathish's present salary?

• A. Rs. 15000
• B. Rs. 18000
• C. Rs. 38000
• D. Rs. 43000
 Ans: C. Sol. Let the original salaries of Prasanna and Sathish be Rs. 2x and Rs. 3x respectively. Then, 2x + 4000 / 3x + 4000 = 40/57 ⇔ 57(2x + 4000) = 40(3x + 4000) ⇔ 6x = 68000 ⇔ 3x = 34000. Sathish's present salary = (3x + 4000) = (34000 + 4000) = Rs.38000.

23. The mean proportional between 234 and 104 is

• A. 12
• B. 39
• C. 54
• D. 156
 Ans: D. Sol. Required mean proportional = √234 x 104 = √13x9x2x13x8 = (13x3x4) = 156.

24. Which of the following ratios is greatest?

• A. 7 : 15
• B. 15 : 23
• C. 17 : 25
• D. 21 : 29
 Ans: D. Sol. 7/15 = 0.466, 15/23 = 0.652, 17/25 = 0.68<,br/> 21/29 = 0.724, Clearly, 0.724 is greatest and therefore, 21 : 29 is greatest.