If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =

Question

If  \frac{2}{5} p + q = 3q - 10,  and if  q = 10 - p,  then  \frac{p}{q} =

(A) 5/7

(B) 3/2

(C) 5/3

(D) 25/6

(E) 6

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • Two equations of p and q: (2/5)p + q = 3q – 10 and q = 10 – p

To find  
We need to determine
 • The value of p/q

Approach and Working out  
Substituting the value of q in the first equation, we get
 • (2/5)p + 10 – p = 3(10 – p) – 10
Or, 2p/5 + 10 – p = 30 – 3p – 10
Or, 2p + 50 – 5p = 150 – 15p – 50
Or, 2p – 5p + 15p = 150 – 50 – 50
Or, 12p = 50
Or, p = 50/12

Hence, q = 10 – p = 10 – 50/12 = 70/12
Therefore, p/q = 50/12: 70/12 = 5/7
 
Thus, option A is the correct answer.

Correct Answer: Option A

AkP1992 · Answer

Given 
(2/5)p + q = 3q - 10 -------i

And 
q= 10-p --------ii

We don't need to find p and q separately

From ii
p+q = 10
Substituting in i

(2/5)p + q = 3q - (p+q)
Rearranging,
(1+2/5)p = q
p/q = 5/7

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MathRevolution · Answer

\frac{2}{5}  p + q = 3q - 10 and q = 10 - p or p + q = 10

=>  \frac{2}{5}  p + q = 3q - (p + q)

=>  \frac{2}{5}  p + p = 3q - q - q

=>  \frac{7}{5}  p = q

=>  \frac{p }{ q}  =  \frac{5}{7}

Answer A

BrushMyQuant · Answer

Given that  \frac{2}{5} p + q = 3q - 10  and q = 10 - p and we need to find the value of  \frac{p}{q} =

\frac{2}{5} p + q = 3q - 10  
=>  \frac{2}{5}  p = 3q - 10 - q = 2q - 10 ...(1)
and q = 10 - p (given)

Putting value of q in (1) we get
 \frac{2}{5}  p = 2*(10 - p) - 10 = 20 - 2p - 10 = 10 - 2p
=> 2p = 5*(10-2p)
=> 2p = 50 - 10p
=> 12p = 50
=> p =  \frac{50}{12}  =  \frac{25}{6}

q = 10 - p = 10 -  \frac{25}{6}  =  \frac{60 - 25}{6}  =  \frac{35}{6}

\frac{p}{q}  = ( \frac{25}{6} ) / ( \frac{35}{6} ) =  \frac{25}{35}  =  \frac{5}{7}

So,  Answer will be A 
Hope it helps!

If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =

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If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =

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