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Ratio and Proportion

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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.
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

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.