Practice | Hashtable

91. If A : B = 2 : 3, B : C = 2 : 4 and C : D = 2 : 5, then A : D is equal to -

A. 1 : 5

B. 2 : 5

C. 3 : 5

D. 2 : 15

Solution:

\begin{aligned} = \frac{A}{B} = \frac{2}{3}, \frac{B}{C} = \frac{2}{4}, \frac{C}{D} = \frac{2}{5} \\ \Rightarrow \frac{A}{D} = (\frac{A}{B} \times \frac{B}{C} \times \frac{C}{D}) \\ \Rightarrow \frac{2}{3} \times \frac{2}{4} \times \frac{2}{5} = \frac{2}{15} \\ \Rightarrow A : D = 2 : 15. \end{aligned}

92. If 3A = 5B and 4B = 6C, then A : C equal to -

A. 2 : 5

B. 3 : 5

C. 4 : 5

D. 5 : 2

Discuss

Solution:

\begin{aligned} = 3A = 5B and 4B = 6C \\ \Rightarrow \frac{A}{B} = \frac{5}{3} and \frac{B}{C} = \frac{6}{4} = \frac{3}{2} \\ \Rightarrow \frac{A}{C} = (\frac{A}{B} \times \frac{B}{C}) = \frac{5}{3} \times \frac{3}{2} = \frac{5}{2} \\ \Rightarrow A : C = 5 : 2 \end{aligned}

93. In a business, the ratio of the capitals of A and B is 2 : 1, that of B and C is 4 : 3 and that of D and C is 6 : 5. Then the ratio of the capitals of A and D is -

A. 9 : 20

B. 3 : 5

C. 5 : 3

D. 20 : 9

Discuss

Solution:

\begin{aligned} = \frac{A}{B} = \frac{2}{1}, \frac{B}{C} = \frac{4}{3}, \frac{C}{D} = \frac{5}{6} \\ \Rightarrow \frac{A}{D} = (\frac{A}{B} \times \frac{B}{C} \times \frac{C}{D}) \\ = (\frac{2}{1} \times \frac{4}{3} \times \frac{5}{6}) \\ = \frac{20}{9} \\ \Rightarrow A : D = 20 : 9 \end{aligned}

94. If a : b = c : d = e : f = 1 : 2, then (3a + 5c + 7e) : (3b + 5d + 7f) is = ?

A. 8 : 7

B. 2 : 1

C. 1 : 4

D. 1 : 2

Discuss

Solution:

a : b = 1 : 2
c : d = 1 : 2
e : f = 1 : 2
∴ a = x, b = 2x, c = x, d = 2x, e = x, f = 2x

\begin{aligned} ∴ \frac{3 \times x + 5 \times 7 + 7 \times x}{3 \times 2 x + 5 \times 2 x + 7 \times 2 x} \times 1 \\ \Rightarrow \frac{15 x}{30 x} \\ \Rightarrow \frac{1}{2} \end{aligned}

95. Of the three numbers, the ration of the first and the second is 8 : 9 and that of the second and third is 3 : 4. If the product of the first and third number is 2400. then the second number is = ?

A. 45

B. 40

C. 24

D. 10

Discuss

Solution:

\begin{aligned} A : B : C \\ 8 : 9 \\ 3 : 4 \\ 8 : 9 : 12 \\ 8 x : 9 x : 12 x \\ ∴ 8 x \times 12 x = 2400 \\ \Rightarrow x^{2} = \frac{2400}{12 \times 8} \\ \Rightarrow x = 5 \\ ∴ B = 9 \times 5 = 45 \end{aligned}

96. The annual income of A and B are in the ratio 4 : 3 and the ratio of their expenditures is 3 : 2. If each of them saves Rs. 600 in the year, the annual income of A is = ?

A. Rs. 4800

B. Rs. 1800

C. Rs. 1200

D. Rs. 2400

Discuss

Solution:

Income Ratio of A and B = 4 : 3
Expenditure ratio of A and B = 3 : 2
Saving Ratio of A and B = 1 : 1
∴1unit = 600
Income of A = 4 × 600 = Rs. 2400

97. If A : B = 7 : 9 and B : C = 5 : 4, then A : B : C is -

A. 7 : 45 : 36

B. 28 :36 : 35

C. 35 : 45 : 36

D. None of these

Discuss

Solution:

\begin{aligned} = A : B = 7 : 9 and \\ B : C = 5 : 4 \\ = (5 \times \frac{9}{5}) : (4 \times \frac{9}{5}) \\ = 9 : \frac{36}{5} . \\ \Rightarrow A : B : C = 7 : 9 : \frac{36}{5} \\ = 35 : 45 : 36. \end{aligned}

98. If A : B = $\frac{1}{2}$ : $\frac{1}{3}$ and B : C = $\frac{1}{2}$ : $\frac{1}{3},$ then A, B, C is equal to -

A. 1 : 2 : 6

B. 2 : 3 : 3

C. 3 : 2 : 6

D. 9 : 6 : 4

Discuss

Solution:

\begin{aligned} = A : B = \frac{1}{2} : \frac{1}{3} = 3 : 2, \\ = B : C = \frac{1}{2} : \frac{1}{3} = 3 : 2 \\ = (3 \times \frac{2}{3}) : (2 \times \frac{2}{3}) \\ = 2 : \frac{4}{3} . \\ \Rightarrow A : B : C = 3 : 2 : \frac{4}{3} \\ = 9 : 6 : 4 \end{aligned}