Simplification - Aptitude MCQ Questions and Solutions with Explanations Page-10 section-2

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91.
If $$\frac{{x + 1}}{{x - 1}}{\text{ = }}\frac{a}{b}$$ and $$\frac{{1 - y}}{{1 + y}}{\text{ = }}\frac{b}{a}{\text{,}}$$ then the value of $$\frac{{x - y}}{{1 + xy}}$$ = ?

A. $$\frac{{2ab}}{{{a^2} - {b^2}}}$$

B. $$\frac{{{a^2} - {b^2}}}{{2ab}}$$

C. $$\frac{{{a^2} + {b^2}}}{{2ab}}$$

D. $$\frac{{{a^2} - {b^2}}}{{ab}}$$

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Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & \frac{{x + 1}}{{x - 1}}{\text{ = }}\frac{a}{b}{\text{ }} \cr & {\text{By componendo and dividendo}} \cr & \frac{{x + 1 + x - 1}}{{x + 1 - x + 1}} = \frac{{a + b}}{{a - b}} \cr & \Rightarrow \frac{{2x}}{2} = \frac{{a + b}}{{a - b}} \cr & \Rightarrow x = \frac{{a + b}}{{a - b}}.....(i) \cr & {\text{Again ,}}\frac{{1 - y}}{{1 + y}}{\text{ = }}\frac{b}{a}{\text{ }} \cr & \Rightarrow \frac{{1 + y}}{{1 - y}} = \frac{a}{b} \cr & \Rightarrow \frac{{1 + y + 1 - y}}{{1 + y - 1 + y}} = \frac{{a + b}}{{a - b}} \cr & \Rightarrow \frac{2}{{2y}} = \frac{{a + b}}{{a - b}} \cr & \Rightarrow \frac{1}{y} = \frac{{a + b}}{{a - b}} \cr & \Rightarrow y = \frac{{a - b}}{{a + b}}.....(ii) \cr & {\text{Subtracting equation (ii) from (i) we get }} \cr & \therefore x - y = \frac{{a + b}}{{a - b}} - \frac{{a - b}}{{a + b}} \cr & \left[ {\because {{\left( {a + b} \right)}^2} - {{\left( {a - b} \right)}^2} = 4ab\,\,\,and\,\,{a^2} - {b^2} = \left( {a - b} \right)\left( {a + b} \right)} \right] \cr & = \frac{{{{\left( {a + b} \right)}^2} - {{\left( {a - b} \right)}^2}}}{{\left( {a - b} \right)\left( {a + b} \right)}} \cr & = \frac{{4ab}}{{{a^2} - {b^2}}} \cr & {\text{Multiply equation (i) and (ii) we get}} \cr & xy = \frac{{a + b}}{{a - b}} \times \frac{{a - b}}{{a + b}} = 1 \cr & \therefore {\text{Expression,}} \cr & {\text{ = }}\frac{{x - y}}{{1 + xy}} = \frac{{\frac{{4ab}}{{{a^2} - {b^2}}}}}{{1 + 1}} \cr &\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{4ab}}{{2\left( {{a^2} - {b^2}} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2ab}}{{{a^2} - {b^2}}} \cr} $$

92.
200 ÷ 25 × 4 + 12 - 3 = ?

A. 35

B. 40

C. 30

D. 41

E. 50

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93.
Evaluate : $$\frac{{\left( {923 - 347} \right)}}{?} = 32$$

A. 35

B. 20

C. 18

D. 15

E. 40

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94.
1559.95 - 7.99 × 24.96 - ?² = 1154

A. 14

B. 24

C. 32

D. 18

E. 8

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95.
Solve $${\text{1}}\frac{4}{5} + 20 - 280 \div 25 = ?$$

A. $$8\frac{1}{5}$$

B. $$9\frac{1}{2}$$

C. $$11\frac{1}{2}$$

D. $$10\frac{3}{5}$$

E. $$12\frac{1}{5}$$

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96.
$$\left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 13 = ?$$

A. 4

B. 1

C. 8

D. 2

E. 5

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97.
If x + y = 2a, then the value of $$\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$$

A. 2

B. 0

C. -1

D. 1

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98.
421 ÷ 35 × 299.97 ÷ 25.05 = ?²

A. 22

B. 24

C. 28

D. 12

E. 18

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99.
Simplify : $$\root 3 \of { - 2197} \,\times $$ $$\root 3 \of { - 125} \,\,\div $$ $$\root 3 \of {\frac{{27}}{{512}}} $$ = ?

A. $$\frac{{492}}{7}$$

B. $$\frac{{520}}{3}$$

C. $$\frac{{554}}{7}$$

D. $$\frac{{571}}{5}$$

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100.
Solve : 128.43 + 30.21 + ? = 173

A. 35.66

B. 29.66

C. 43.66

D. 24.66

E. 14.36

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Simplification - Aptitude MCQ Questions and Solutions with Explanations

91. If $$\frac{{x + 1}}{{x - 1}}{\text{ = }}\frac{a}{b}$$ and $$\frac{{1 - y}}{{1 + y}}{\text{ = }}\frac{b}{a}{\text{,}}$$ then the value of $$\frac{{x - y}}{{1 + xy}}$$ = ?

Answer & Solution

92. 200 ÷ 25 × 4 + 12 - 3 = ?

Answer & Solution

93. Evaluate : $$\frac{{\left( {923 - 347} \right)}}{?} = 32$$

Answer & Solution

94. 1559.95 - 7.99 × 24.96 - ?2 = 1154

Answer & Solution

95. Solve $${\text{1}}\frac{4}{5} + 20 - 280 \div 25 = ?$$

Answer & Solution

96. $$\left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 13 = ?$$

Answer & Solution

97. If x + y = 2a, then the value of $$\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$$

Answer & Solution

98. 421 ÷ 35 × 299.97 ÷ 25.05 = ?2

Answer & Solution

99. Simplify : $$\root 3 \of { - 2197} \,\times $$ $$\root 3 \of { - 125} \,\,\div $$ $$\root 3 \of {\frac{{27}}{{512}}} $$ = ?

Answer & Solution

100. Solve : 128.43 + 30.21 + ? = 173

Answer & Solution

Read More Section(Simplification)

91.
If $$\frac{{x + 1}}{{x - 1}}{\text{ = }}\frac{a}{b}$$ and $$\frac{{1 - y}}{{1 + y}}{\text{ = }}\frac{b}{a}{\text{,}}$$ then the value of $$\frac{{x - y}}{{1 + xy}}$$ = ?

92.
200 ÷ 25 × 4 + 12 - 3 = ?

93.
Evaluate : $$\frac{{\left( {923 - 347} \right)}}{?} = 32$$

94.
1559.95 - 7.99 × 24.96 - ?² = 1154

95.
Solve $${\text{1}}\frac{4}{5} + 20 - 280 \div 25 = ?$$

96.
$$\left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 13 = ?$$

97.
If x + y = 2a, then the value of $$\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$$

98.
421 ÷ 35 × 299.97 ÷ 25.05 = ?²

99.
Simplify : $$\root 3 \of { - 2197} \,\times $$ $$\root 3 \of { - 125} \,\,\div $$ $$\root 3 \of {\frac{{27}}{{512}}} $$ = ?

100.
Solve : 128.43 + 30.21 + ? = 173