## Ratio Questions and Answers Part-8

1. A sum of Rs. 1240 is distributed among A, B and C such that the ratio of amount received by A and B is 6 : 5 and that of B and C is 10 : 9 respectively. Find the share of C ?
a) Rs. 480
b) Rs. 360
c) Rs. 400
d) Rs. 630

Explanation: A : B = 6 : 5
B : C = 10 : 9
A : B = 6 : 5 (multiply with 2)
i.e. A : B = 12 : 10
A : B : C = 12 : 10 : 9
12x + 10x + 9x = 1280
x = 40
Share of C = 9 × 40 = 360

2. If x : 7.5 = 7 : 17.5, then the value of x is -
a) 1
b) 2.5
c) 3
d) 3.5

Explanation:
\eqalign{ & = x:7.5 = 7:17.5 \cr & 17.5x = 7.5 \times 7 \cr & x = \frac{{7.5 \times 7}}{{17.5}} \cr & = 3 \cr}

3. The value of $$x$$ where $$x$$ : $$2\frac{1}{3}$$ :: $$21$$ : $$50$$ is -
a) $$1\frac{1}{{49}}$$
b) $$1\frac{1}{{50}}$$
c) $$\frac{{49}}{{50}}$$
d) $$\frac{{27}}{{50}}$$

Explanation:
\eqalign{ & = x:2\frac{1}{3}::21:50 \cr & 50x = \frac{7}{3} \times 21 \cr & 50x = 49 \cr & x = \frac{{49}}{{50}} \cr}

4. If $$\sqrt 2$$ : $$\left( {1 + \sqrt 3 } \right)$$  :: $$\sqrt 6$$ : $$x$$, then $$x$$ is equal to -
a) $$\sqrt 3 + 3$$
b) $$1 - \sqrt 3$$
c) $$1 + \sqrt 3$$
d) $$\sqrt 3 - 3$$

Explanation:
\eqalign{ & = \sqrt 2 :\left( {1 + \sqrt 3 } \right)::\sqrt 6 :x \cr & \sqrt {2}x = \sqrt 6 \left( {1 + \sqrt 3 } \right) \cr & x = \frac{{\sqrt 6 \left( {1 + \sqrt 3 } \right)}}{{\sqrt 2 }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 3 \left( {1 + \sqrt 3 } \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 3 + 3 \cr}

5. In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 gm of alloy, then the ratio of copper and zinc will be = ?
a) 2 : 1
b) 2 : 3
c) 3 : 2
d) 1 : 2

Explanation: The ratio of copper and zinc is 5 : 2
i.e 5x : 2x
Quantity of initial mixture = 17.5 kg
5x + 2x = $$\frac{35}{2}$$
⇒ x = $$\frac{5}{2}$$
Quantity of Copper in initial mixture
\eqalign{ & = \frac{5}{2} \times 5 \cr & = \frac{{25}}{2}kg \cr}
Quantity of Zinc in initial mixture
\eqalign{ & = \frac{5}{2} \times 2 \cr & = 5\,kg \cr}
Now after adding 1.250 kg of zinc
= 5 + 1.250
= 6.250 kg
= $$\frac{{25}}{4}kg$$
New Ratio of copper : zinc
\eqalign{ & = \frac{{25}}{2}:\frac{{25}}{4} \cr & = 2:1 \cr}

6. If A : B = $$\frac{1}{2}$$ : $$\frac{3}{8},$$  B : C = $$\frac{1}{3}$$ : $$\frac{5}{9}$$ and C : D = $$\frac{5}{6}$$ : $$\frac{3}{4},$$  then the ratio A : B : C : D is
a) 4 : 6 : 8 : 10
b) 8 : 6 : 10 : 9
c) 6 : 8 : 9 : 10
d) 6 : 4 : 8 : 10

Explanation:
\eqalign{ & {\text{A}}:{\text{B}} = \frac{1}{2}:\frac{3}{8} = 4:3, \cr & {\text{B}}:{\text{C}} = \frac{1}{3}:\frac{5}{9} = 3:5, \cr & {\text{C}}:{\text{D}} = \frac{5}{6}:\frac{3}{4} = 10:9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5:\frac{9}{2}. \cr & {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & = 4:3:5:\frac{9}{2} \cr & = 8:6:10:9 \cr}

7. If p : q : r = 1 : 2 : 4, then $$\sqrt {5{p^2} + {q^2} + {r^2}}$$     is equal to
a) 5
b) 2q
c) 5p
d) 4r

Explanation:
\eqalign{ & {\text{p}}:{\text{q}}:{\text{r}} \cr & 1:2:4 \cr & x:2x:4x \cr & \sqrt {5{p^2} + {q^2} + {r^2}} \cr & = \sqrt {5{x^2} + 4{x^2} + 16{x^2}} \cr & = \sqrt {25{x^2}} \cr & = 5x \cr & = 5p \cr}

8. The mean proportion between $$\left( {3 + \sqrt 2 } \right)$$   and $$\left( {12 - \sqrt {32} } \right)$$   is = ?
a) $$\sqrt 7$$
b) $$2\sqrt 7$$
c) 6
d) $$\frac{{15 - 3\sqrt 2 }}{2}$$

Explanation:
\eqalign{ & \left( {3 + \sqrt 2 } \right):x:\left( {12 - \sqrt {32} } \right) \cr & a:b:c \cr & {\text{mean proportion}} \cr & {b^2} = a \times c \cr & {x^2} = \left( {3 + \sqrt 2 } \right) \times \left( {12 - \sqrt {32} } \right) \cr & {x^2} = \left( {3 + \sqrt 2 } \right) \times \left( {12 - 4\sqrt 2 } \right) \cr & {x^2} = \left( {3 + \sqrt 2 } \right) \times 4\left( {3 - \sqrt 2 } \right) \cr & {x^2} = 4 \times \left\{ {{{\left( 3 \right)}^2} - {{\left( {\sqrt 2 } \right)}^2}} \right\} \cr & {x^2} = 28 \cr & x = 2\sqrt 7 \cr}

9. a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is = ?
a) 6
b) 9
c) 12
d) $$\frac{{66}}{7}$$

\eqalign{ & a:b:c \cr & 2:3:4 \cr & {\text{Let }}2x:3x:4x \cr & 2a - 3b + 4c = 33 \cr & 2 \times 2x - 3 \times 3x + 4 \times 4x = 33 \cr & 4x - 9x + 16x = 33 \cr & 11x = 33 \cr & x = 3 \cr & {\text{c}} \Rightarrow 4 \times 3 = 12 \cr}
\eqalign{ & \frac{7}{8} = \frac{{35}}{x} \Rightarrow 35 \times 8 \cr & x = \frac{{35 \times 8}}{7} = 40 \cr}