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Ratio and Proportion

Aptitude

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

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.