1. If 60% A = $$\frac{3}{4}$$ of B, then A : B is
a) 4 : 5
b) 5 : 4
c) 9 : 20
d) 20 : 9
Explanation:
$$\eqalign{ & {\text{60}}\% \,{\text{of}}\,{\text{A}} = \frac{{\text{3}}}{{\text{4}}}\,{\text{of}}\,{\text{ B}} \cr & \Rightarrow \frac{{60}}{{100}}{\text{A}} = \frac{3}{4}\,{\text{B}} \cr & \frac{{\text{3}}}{{\text{5}}}{\text{A = }}\frac{{\text{3}}}{{\text{4}}}\,{\text{B}} \cr & \frac{{\text{A}}}{{\text{B}}}{\text{ = }}\frac{{\text{3}}}{{\text{4}}} \times \frac{{\text{5}}}{{\text{3}}} \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{5}{4} \cr} $$
A : B = 5 : 4
2. Which of the following represents ab = 64?
a) 8 : a = 8 : b
b) a : 16 = 6 : 4
c) a : 8 = b : 8
d) 32 : a = b : 2
Explanation: A = 8 : a = 8 : b ⇒ 8a = 8b ⇒ a = b.
B = a : 16 = b : 4 ⇒ 4a = 16b ⇒ a = 4b
C = a : 8 = b : 8 ⇒ 8a = 8b ⇒ b = a
D = 32 : a = b : 2 ⇒ ab =64
3. The ratio of boys and girls in a club is 3 : 2. Which of the following could be the actual number of members ?
a) 16
b) 18
c) 24
d) 25
Explanation: The total number of members must be a multiple of the sum ratio terms.
3 + 2 = 5
and 25 is a multiple of 5
4. If m : n = 3 : 2, then (4m + 5n) : (4m - 5n) is equal to = ?
a) 4 : 9
b) 9 : 4
c) 11 : 1
d) 9 : 1
Explanation:
$$\eqalign{ & m:n = 3:2 \cr & \frac{m}{n} = \frac{3}{2} \cr & \frac{{4m + 5n}}{{4m - 5n}} \cr & \frac{{n\left( {4\frac{m}{n} + 5} \right)}}{{n\left( {4\frac{m}{n} - 5} \right)}} \cr & \frac{{4 \times \frac{3}{2} + 5}}{{4 \times \frac{3}{2} - 5}} \cr & \frac{{6 + 5}}{{6 - 5}} \cr & = \frac{{11}}{1} \cr & = 11:1 \cr} $$
5. The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is = ?
a) 21 : 19
b) 22 : 9
c) 11 : 9
d) 11 : 18
Explanation : A + B = 40
A - B = 4
A = 22
B = 18
A : B = 22 : 18
= 11 : 9
6. If A : B = 2 : 3, B : C = 4 : 5 and C : D = 5 : 9 then A : D is equal to:
a) 11 : 17
b) 8 : 27
c) 5 : 9
d) 2 : 9
Explanation:
$$\eqalign{ & \frac{A}{D} = {\frac{A}{B}} \times {\frac{B}{C}} \times {\frac{C}{D}} \cr & \,\,\,\,\,\,\,\,\, = {\frac{2}{3}} \times {\frac{4}{5}} \times {\frac{5}{9}} \cr & \,\,\,\,\,\,\,\,\, = \frac{{ {2 \times 4 \times 5} }}{{ {3 \times 5 \times 9} }} \cr & \,\,\,\,\,\,\,\,\, = \frac{8}{{27}} \cr & \,\,\,\,\,\,\,\,\, = 8:27 \cr} $$
7. In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is
a) 1 : 2
b) 3 : 4
c) 1 : 4
d) 3 : 5
Explanation: Girls : boys = 6 : 5
Hence, girls = $$6 \times \frac{{66}}{{11}}$$ = 36
Boys = 30
New ratio, 30 : (36 + 4) = 3 : 4
8. What must be added to each term of the ratio 7 : 11, So as to make it equal to 3 : 4?
a) 8
b) 7.5
c) 6.5
d) 5
Explanation:
$$\eqalign{ & {\text{Let }}x{\text{ be added to each term}}. \cr & \frac{{ {7 + x} }}{{11 + x}} = \frac{3}{4} \cr & \,33 + 3x = 28 + 4x \cr & \,x = 5 \cr} $$
9. Two numbers are in ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. The smaller number is
a) 39
b) 49
c) 66
d) 77
Explanation: Let the numbers be 7x and 11x.
$$\eqalign{ & \frac{{ {7x + 7} }}{{ {11x + 7} }} = \frac{2}{3} \cr & \,22x + 14 = 21x + 21 \cr & \,x = 7 \cr & {\text{Smaller}}\,{\text{number}} = 49 \cr} $$
10. Two numbers are in ratio P : Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to $$\frac{{\text{R}}}{{\text{S}}}$$. again, when 1 is added to both the numerator and denominator, it becomes $$\frac{1}{2}$$. Find the sum of P and Q.
a) 3
b) 4
c) 5
d) 6
Explanation: We will solve this question through options
Taking Option A:
It has P + Q = 3.
The possible value of $$\frac{{\text{P}}}{{\text{Q}}}$$ is $$\frac{1}{2}$$ or $$\frac{2}{1}$$
Using $$\frac{1}{2}$$, we see that on adding 2 in both the numerator and denominator we get $$\frac{3}{4}$$ (not required value)
Similarly we check for $$\frac{2}{1}$$, this will also not give the required value
Option B:
We have $$\frac{1}{3}$$ possible ratio
Then, we get the final value as $$\frac{3}{5}$$ (not = to $$\frac{1}{2}$$)
Hence, rejected
Option C:
Here we have $$\frac{1}{4}$$ or $$\frac{2}{3}$$
Checking for $$\frac{1}{4}$$ we get $$\frac{3}{6}$$ = $$\frac{1}{2}$$
Hence, the option c is correct