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Two numbers x and y (x > y) such that their sum is equal to three times their difference. Then value of \( \Large \frac{3xy}{2 \left(x^{2}-y^{2}\right) } \) will be;

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

Correct Answer:


B) 1

Description for Correct answer:
x > y

given :-

\( \Large x+y = 3 \left(x-y\right) \)

=> \( \Large x + y = 3x - 3y \)

=> \( \Large x - 3x = -3y - y \)

=> \( \Large -2x = -4y => x = 2y \)

Therefore, \( \Large \frac{3xy}{2 \left(x^{2}-y^{2}\right) }=\frac{3 \times 2y \times y}{2 \left( \left(2y\right)^{2}-y^{2} \right) } \)

= \( \Large \frac{6y^{2}}{2 \times \left(4y^{2}-y^{2}\right) } \)

= \( \Large \frac{6y^{2}}{6y^{2}} = 1 \)

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

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Similar Questions

1). The value of \( \Large \left(1+\frac{1}{x}\right) \left(1+\frac{1}{x+1}\right) \left(1+\frac{1}{x+2}\right) \left(1+\frac{1}{x+3}\right) \) is:

A). \( \Large 1+\frac{1}{x+4} \)

B). x+4

C). \( \Large \frac{1}{x} \)

D). \( \Large \frac{x+4}{x} \)

2). If \( \Large x = 7-4\sqrt{3} \), then the value of \( \Large x+\frac{1}{x} \)

A). \( \Large 3\sqrt{3} \)

B). \( \Large 8\sqrt{3} \)

C). \( \Large 14+8\sqrt{3} \)

D). 14

3). If \( \Large \frac{a}{b}=\frac{2}{3}\ and\ \frac{b}{c}=\frac{4}{5} \) , then the ratio \( \Large \frac{a+b}{b+c} \) equal to:

A). \( \Large \frac{20}{27} \)

B). \( \Large \frac{27}{20} \)

C). \( \Large \frac{6}{8} \)

D). \( \Large \frac{8}{6} \)

4). If \( \Large a\ast b=2 \left(a+b\right) \), then \( \Large 5\ast 2 \) is equal to:

A). 3

B). 10

C). 14

D). 20

5). If \( \Large \frac{2a+b}{a+4b}=3 \), then find the value of \( \Large \frac{a+b}{a+2b} \)

A). \( \Large \frac{5}{9} \)

B). \( \Large \frac{2}{7} \)

C). \( \Large \frac{10}{9} \)

D). \( \Large \frac{10}{7} \)

6). If \( \Large a\ast b=a+b+ab \), then \( \Large 3\ast 4-2\ast 3 \) is equal to:

A). 6

B). 8

C). 10

D). 12

7). If \( \Large x \circledast y = 3x+2y \), then \( \Large 2 \circledast 3+3 \circledast 4 \) is equal to

A). 18

B). 29

C). 32

D). 38

8). If a : b = 2 : 3 and b : c = 4 : 5, find \( \Large a^{2} : b^{2} : bc \)

A). 4 : 9 : 45

B). 16 : 36 : 45

C). 16 : 36 : 20

D). 4 : 36 : 40

9). If \( \Large A : B = \frac{1}{2} : \frac{3}{8},\ B : C = \frac{1}{3} : \frac{5}{9},\ C : D = \frac{5}{6} : \frac{3}{4} \), then find the ratio of A : B : C : D

A). 6 : 4 : 8 : 10

B). 6 : 8 : 9 : 10

C). 8 : 6 : 10 : 9

D). 4 : 6 : 8 : 10

10). If A : B : C = 2 : 3 : 4, then \( \Large \frac{A}{B} : \frac{B}{C} : \frac{C}{A} \) is equal to

A). 8 : 9 : 16

B). 8 : 9 : 12

C). 8 : 9 : 24

D). 4 : 9 : 16