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

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GMAT Club team member
Status: GMAT Club Team Member
Affiliations: GMAT Club
Joined: 02 Nov 2016
Posts: 5905
GPA: 3.62
If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =  [#permalink]

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20 Mar 2020, 23:42
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:03) correct 31% (02:20) wrong based on 16 sessions

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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

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Joined: 04 Jan 2015
Posts: 3367
Re: If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =  [#permalink]

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21 Mar 2020, 07:17
1

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.

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Re: If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =   [#permalink] 21 Mar 2020, 07:17