Tricks to Solve Ratio and Proportion (Important Facts and Formula) for Bank, SSC, Railway and Other Government Job related Competitive Exam. Ratio and Proportion questions are commonly asked in all the Competitive Exam. In this Article we will Discuss some Tricks to Solve Ratio and Proportion Questions Quickly.
1. 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.
In the ratio a:b, we call a as the first term or
antecedent and b, the second
term or consequent.
Ex. The
ratio 5: 9 represents 5/9 with antecedent = 5, consequent = 9.
Rule: The
multiplication or division of each term of a ratio by the same non-zero number does not affect
the ratio.
Ex. 4: 5 = 8: 10 = 12: 15 etc. Also, 4: 6 = 2: 3.
2. PROPORTION: The equality of two ratios is called proportion.
If a: b = c: d, we write, a: b:: c : d and
we say that a, b, c, d are in proportion . Here a and d are called extremes, while b and c are called
mean terms.
Product of means
= Product of extremes.
Thus, a: b:: c : d <=> (b x c) = (a x d).
3. (i) Fourth Proportional: If a : b = c: d, then
d is called the fourth proportional
to
a, b, c.
(ii) Third Proportional: If a: b = b:
c, then c is called the third proportional to
a
and b.
(iii) Mean Proportional: Mean proportional between a and b is
square root of ab
4. (i) COMPARISON OF RATIOS:
We say that (a: b) > (c: d) <=> (a/b)>(c /d).
(ii)
COMPOUNDED RATIO:
The
compounded ratio of the ratios (a: b), (c: d), (e : f) is (ace:
bdf)
5. (i)
Duplicate ratio of (a : b) is (a2 : b2).
(ii) Sub-duplicate ratio of (a : b) is (√a : √b).
(iii)Triplicate ratio of (a : b) is (a3 : b3).
(iv) Sub-triplicate ratio of (a : b) is (a ⅓ : b ⅓ ).
(v) If (a/b)=(c/d), then
((a+b)/(a-b))=((c+d)/(c-d)) (Componendo
and dividendo)
6. VARIATION:
(i) We say that x is directly proportional to y, if
x = ky for some constant k and
we write, x µ y.
(ii) We say that x is
inversely proportional to y, if xy = k for some constant k and
we write, x∞(1/y)
8.A:B & B:C & C:D Then A:B:C:D = ?
SOLVED PROBLEMS
Ex. 1. 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.
Ex. 2. Find:
(i)
the fourth proportional to 4, 9, 12;
(ii)
the third proportional to 16 and 36;
(iii)
the mean proportional between 0.08 and
0.18.
Sol.
i) Let
the fourth proportional to 4, 9, 12 be x.
Then, 4 : 9 : : 12 : x ó 4
x x=9x12 ó
X=(9 x 12)/14=27;
Fourth proportional to 4, 9, 12 is 27.
(ii) Let
the third proportional to 16 and 36 be x.
Then, 16 : 36 : : 36 : x ó16 x x = 36 x 36 ó x=(36 x 36)/16 =81
Third proportional to 16 and 36 is 81.
(iii) Mean
proportional between 0.08 and 0.18
Ö0.08
x 0.18 =Ö8/100
x 18/100= Ö144/(100
x 100)=12/100=0.12
Ex. 3. If x : y = 3 : 4, find
(4x + 5y) : (5x - 2y).
Sol. X/Y=3/4 ó (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2)
=(4(3/4)+5)/(5(3/4)-2)
=(3+5)/(7/4)=32/7
Ex. 4. Divide Rs. 672 in the
ratio 5 : 3.
Sol.
Sum of ratio terms = (5 + 3) = 8.
First part = Rs. (672 x (5/8)) = Rs. 420; Second part = Rs. (672 x
(3/8)) = Rs. 252.
Ex. 5. 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.
Ex. 6. A bag contains 50 p, 25
P and 10 p coins in the ratio 5: 9: 4, amounting to
Rs. 206. Find the number of coins
of each type.
Sol.
Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively.
(5x/2)+( 9x/ 4)+(4x/10)=206ó 50x
+ 45x + 8x = 4120ó1O3x = 4120 óx=40.
Number of 50 p coins = (5 x 40) = 200; Number of 25 p coins = (9 x 40) =
360;
Number of 10 p coins = (4 x 40) = 160.
Ex.
7. A mixture contains alcohol and water in the ratio 4
: 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find
the quantity of alcohol in the given mixture
Sol.
Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5)=4/5 ó20x=4(3x+5)ó8x=20 óx=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
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