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If \( \Large \frac{x}{y}=\frac{3}{4} \), the value of \( \Large \frac{6}{7}+\frac{y-x}{y+x} \) is:

A) 1
B) \( \Large \frac{2}{7} \)
C) \( \Large \frac{3}{7} \)
D) \( \Large 1\frac{3}{7} \)

Correct Answer:

A) 1

Description for Correct answer:
\( \Large \frac{x}{y}=\frac{3}{4}, \frac{6}{7}+\frac{y-x}{y+x}=? \)

= \( \Large \frac{6}{7}+\frac{y \left(1-\frac{x}{y}\right) }{y \left(1+\frac{x}{y}\right) } \)

= \( \Large \frac{6}{7}+\frac{y \left(1-\frac{3}{4}\right) }{y \left(1+\frac{3}{4}\right) } \)

= \( \Large \frac{6}{7}+\left[ \frac{4-3}{4} \times \frac{4}{ \left(4+3\right) } \right] \)

= \( \Large \frac{6}{7}+\frac{1}{7} = \frac{7}{7} = 1 \)

Part of solved Elementary Mathematics questions and answers : >> Elementary Mathematics

Comments

Similar Questions

1). If \( \Large x=7-4\sqrt{3} \), then \( \Large \sqrt{x}+\frac{1}{\sqrt{x}} \) is equal to:

A). 1

B). 2

C). 3

D). 4

2). If \( \Large a=\frac{\sqrt{5}+1}{\sqrt{5}-1}\ and\ b=\frac{\sqrt{5}-1}{\sqrt{5}+1} \), then the value of \( \Large \frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}} \)

A). \( \Large \frac{3}{4} \)

B). \( \Large \frac{4}{3} \)

C). \( \Large \frac{3}{5} \)

D). \( \Large \frac{5}{3} \)

3). If a=4.36, b=2.39 and c=1.97, then the value of \( \Large a^{3}-b^{3}-c^{3}-3abc \) is

A). 3.94

B). 2.39

C). 0

D). 1

4). If \( \Large \frac{3a+5b}{3a-5b}=5 \), then a:b is equal to:

A). 2:1

B). 2:3

C). 1:3

D). 5:2

5). If p:q=r:s=t:u=2:3, then \( \Large \left(mp+nr+ot\right): \left(mq+ns+ou\right) \) equals

A). 3:2

B). 2:3

C). 1:3

D). 1:2

6). If x:y=3:4, then \( \Large \left(7x+3y\right): \left(7x-3y\right) \) is equal to:

A). 5:2

B). 4:3

C). 11:3

D). 37:19

7). For what value(s) of a is \( \Large x+\frac{1}{4}\sqrt{x}+a^{2} \) a perfect square?

A). \( \Large \pm \frac{1}{18} \)

B). \( \Large \frac{1}{8} \)

C). \( \Large -\frac{1}{5} \)

D). \( \Large \frac{1}{4} \)

8). If \( \Large a\ne b \), then which of the following statements is true?

A). \( \Large \frac{a+b}{2}=\sqrt{ab} \)

B). \( \Large \frac{a+b}{2}<\sqrt{ab} \)

C). \( \Large \frac{a+b}{2}>\sqrt{ab} \)

D). All of the above

9). If x, y are two positive real number and , then which of the following relations is true?

A). \( \Large x^{3}=y^{4} \)

B). \( \Large x^{3}=y \)

C). \( \Large x=y^{4} \)

D). \( \Large x^{20}=y^{15} \)

10). If \( \Large x=\frac{\sqrt{3}}{2} \), then \( \Large \frac{\sqrt{1+x}}{1+\sqrt{1+x}}+\frac{\sqrt{1-x}}{1-\sqrt{1-x}} \) is equal to:

A). 1

B). \( \Large 2/\sqrt{3} \)

C). \( \Large 2-\sqrt{3} \)

D). 2