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Andy and Bob originally had pens in the ratio 3:7. Bob gave

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Andy and Bob originally had pens in the ratio 3:7. Bob gave [#permalink] New post   20 Sep 2019, 08:18
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Andy and Bob originally had pens in the ratio 3:7. Bob gave some of his pens to Andy. As a result, the ratio of number of pens of Andy and Bob became 2:3. What fraction of his pens did Bob gave to Andy?

A. 1/5
B. 2/9
C. 1/7
D. 2/7
E. 1/6­
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Re: Andy and Bob originally had pens in the ratio 3:7. Bob gave [#permalink] New post   20 Sep 2019, 08:57
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let Andy has \(3x\) pens, and Bob has \(7x\) pens, and Bob gave \(y\) pens to Andy

\(\frac{3x+y}{7x-y} = \frac{2}{3}\)
so \(y = x\), and fraction of his pens did Bob gave to Andy =\(\frac{y}{7x} = \frac{x}{7x} = \frac{1}{7}\)
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Re: Andy and Bob originally had pens in the ratio 3:7. Bob gave [#permalink] New post   05 Nov 2020, 23:59
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Dillesh4096 wrote:
Andy and Bob originally had pens in the ratio 3:7. Bob gave some of his pens to Andy. As a result, the ratio of number of pens of Andy and Bob became 2:3. What fraction of his pens did Bob gave to Andy?

A. 1/5
B. 2/9
C. 1/7
D. 2/7
E. 1/6

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SUBSTITUTION
Let the number of pens be some multiple of (3+7) or 10, say 100.
so A:B=30:70....
After B gave some pens, it becomes 2:3 or 40:60. Clearly B gave 70-60 or 10.
10 as fraction of 70 =\(\frac{10}{70}=\frac{1}{7}\)

ALGEBRAIC
A:B = 3:7 or 3x:7x
Let B gives y pens, so (3x+y):(7x-y)=2:3..
\(\frac{(3x+3y)}{(7x-y)}=\frac{2}{3}\)..
\(9x+3y=14x-2y\)
\(5x=5y....x=y\)
So y as a fraction of 7x => \(\frac{y}{7x}=\frac{x}{7x}=\frac{1}{7}\)

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Re: Andy and Bob originally had pens in the ratio 3:7. Bob gave [#permalink] New post   06 Nov 2020, 00:05
Suppose Andy = A, Bob = B
We are looking for X/B.
Original Ratio of Pens; A/ B = 3/7 ....(a)
Suppose, x pens are given to Andy by Bob, then new ratio is (A + x)/ (B - x) = 2/3 ..... (b)
Simplify eq. (b) gives 3A + 3X = 2B - 2X
Replace A = 3B/7 in the above equation from eq. (a)
3(3B/7) + 3x = 2B - 2x
9B/7 + 3x = 2B - 2X
5x = 5B/7
X/B = 1/7
Answer is c.
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Re: Andy and Bob originally had pens in the ratio 3:7. Bob gave [#permalink] New post   06 Nov 2020, 00:08
Ans: 1/7

Setting up the equation we get (3+X)/ (7-X) = 2/3, where X = No of pens that Bob gave to Andy

Solving for X, we get X =1

So the fraction of pens that Bob gave= 1/7
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Re: Andy and Bob originally had pens in the ratio 3:7. Bob gave [#permalink] New post   13 Feb 2024, 07:03
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Re: Andy and Bob originally had pens in the ratio 3:7. Bob gave [#permalink]
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