FeedBack Form

Your Name :
Your Email :
Your Location :
Your Message :
   
FeedBack

Ratio and Proportion

Follow Us
 

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.
2. 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.