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The solution of the equations \( \Large \frac{p}{x}+\frac{q}{y} \ and \ \frac{q}{x}+\frac{p}{y} \) n is

A) \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \)
B) \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \)
C) \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \)
D) \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \)

Correct Answer:



C) \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \)

Description for Correct answer:

\( \Large \frac{p}{x}+\frac{q}{y}=m \) ...(i)

\( \Large \frac{q}{x}+\frac{p}{y}=n \) ...(ii)

On multiplying Eq. (i) by q and Eq. (ii) by p and subtracting, we get

\( \Large \frac{pq}{x}+\frac{q^{2}}{y}=mq \)

\( \Large \frac{pq}{x}+\frac{p^{2}}{y}=np \)

\( \Large \frac{q^{2}}{y}-\frac{p^{2}}{y}=mq-np \)

Therefore, \( \Large q^{2}-p^{2}=y \left(mq-np\right) \)

Therefore, \( \Large y = \frac{q^{2}-p^{2}}{mq-np}=\frac{p^{2}-q^{2}}{np-mq} \)

Again, on multiplying Eq. (i) by p and Eq. (ii) by q and subtracting, we get

\( \Large \frac{p^{2}}{x}+\frac{pq}{y}=mp \)

\( \Large \frac{q^{2}}{x}+\frac{pq}{y}=nq \)

\( \Large \frac{p^{2}}{x}-\frac{q^{2}}{x}=mp-nq \)

= \( \Large p^{2}-q^{2}=x \left(mp-nq\right) \)

= \( \Large x = \frac{p^{2}-q^{2}}{mp-nq} \)

Therefore, \( \Large x = \frac{p^{2}-q^{2}}{mp-nq} \)

and \( \Large y = \frac{p^{2}-q^{2}}{np-mq} \)

Part of solved Linear Equations questions and answers : >> Aptitude >> Linear Equations

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Similar Questions

1). If \( \Large \frac{3}{x+y}+\frac{2}{x-y}=2 \) and \( \Large \frac{9}{x+y}-\frac{4}{x-y}=1 \), then what is the value of \( \Large \frac{x}{y} \)?

A). \( \Large \frac{3}{2} \)

B). 5

C). \( \Large \frac{2}{3} \)

D). \( \Large \frac{1}{5} \)

2). If \( \Large \frac{a}{b}-\frac{b}{a}=\frac{x}{y} \) and \( \Large \frac{a}{b}+\frac{b}{a}= x - y \) , then what is the value of x?

A). \( \Large \frac{a+b}{a} \)

B). \( \Large \frac{a+b}{b} \)

C). \( \Large \frac{a-b}{a} \)

D). None of these

3). If \( \Large \frac{x}{2}+\frac{y}{3}=4 \) and \( \Large \frac{2}{x}+\frac{3}{y}=1 \) then what is x + y equal to?

A). 11

B). 10

C). 9

D). 8

4). A mason can build a tank in 12 h. After working for 6 h, he took the help of a boy and finished the work in another 5 h. The time that the boy will take alone to complete the work is

A). 30 h

B). 45 h

C). 60 h

D). 64 h

5). A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work ?

A). 36

B). 12

C). 18

D). 9

6). A does 20% less work than B. If A can complete a piece of work in \(7\frac{1}{2}\)h, then B can do it in

A). 4 h

B). 6 h

C). 8 h

D). 10 h

7). A takes twice as much time as B and C takes thrice as much time as B to finish a work. Working together, they can finish the work , in 12 days. Find the number of days needed for A to do the work alone.

A). 20

B). 22

C). 33

D). 44

8). A is thrice as good a workman as B and therefore is able to finish a job in 30 days less than B. How many days will they take to finish the job working together?

A). \( \Large 10\frac{1}{4} \)

B). \( \Large 11\frac{3}{4} \)

C). \( \Large 11\frac{1}{4} \)

D). \( \Large 11 \frac{1}{3} \)

9). X can do a work in 16 days. In how many days will the work be completed by Y, if the efficiency of Y is 60% more than that of X?

A). 10 days

B). 12 days

C). 25 days

D). 30 days

10). 10 men and 8 women together can complete a work in 5 days. Work done by one woman in a day is equal to half the work done by a man in 1 day. How many days will it take for 4 men and 6 women to complete that work?

A). 12 days

B). 10 days

C). \( \Large \frac 8{2}{3} \)days

D). \( \Large \frac 4{3}{4} \)days