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# Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat

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Math Expert
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Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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16 May 2016, 01:46
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82% (01:44) correct 18% (02:18) wrong based on 192 sessions

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Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

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Posts: 79
Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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16 May 2016, 01:58
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

Reqd. ratio = 2 : 1.5 i.e. 4 : 3 between paint and water respectively.
6 litres of paint which is half water(3 litres) and half paint (3 litres)

Right now the ratio is 1:1
Looking at the options,
A. Paint : Water = 4 : 3 which is the reqd. ratio . Correct Answer
B. Paint : Water = 3 : 4
C. Paint : Water = 4 : 3.5
D. Paint : Water = 3.5 : 4
E. Paint : Water = 3.5 : 3

Math Expert
Joined: 02 Aug 2009
Posts: 7036
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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16 May 2016, 02:04
2
1
Bunuel wrote:
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

Hi,

two ways-
1) based on choice-
water and paint are in ratio 1:1.. we have to make it 2:1.5 or 4:3..
so clearly paint has to be added to bring up the ratio of paint..
ONLY A and E are left

Quantity P:W is 3:3 it has to be converted to 4:3..
so clearly 1 liter of P is to be added
ans A

2) Proper method-
existing ratio = 3:3..
add y to convert to 4:3..
so $$\frac{3+y}{3}= \frac{4}{3}$$....
$$9+3y=12.................3y=12-9...................y=1$$
ans A
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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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25 May 2017, 10:12
Required ratio = Paint/Water = 2/1.5 = 4/3
Right now, paint = 3 litres and water = 3 litres

lets say 'x' litres of paint need to be added to make the desired ratio. Then we have:
(3+x)/3 = 4/3 Or 3+x = 4 or x = 1

VP
Joined: 07 Dec 2014
Posts: 1114
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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Updated on: 04 Jul 2018, 10:12
Bunuel wrote:
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

let p=litres of paint to be added
3+p=4/7*(6+p)
p=1 litre paint
A

Originally posted by gracie on 25 May 2017, 10:29.
Last edited by gracie on 04 Jul 2018, 10:12, edited 1 time in total.
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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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31 May 2017, 18:03
1
Bunuel wrote:
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

We are given that the painter needs a ratio of paint to water of 2x : 1.5x.

However, he actually has 3 litres of paint and 3 litres of water, which make a ratio of 1 : 1. To make the correct ratio of paint to water, he must add more paint.

We can let n = the number of litres of paint he must add.

(3 + n)/3 = 2x/1.5x

(3 + n)/3 = 2/1.5

1.5(3 + n) = 6

4.5 + 1.5n = 6

1.5n = 1.5

n = 1

Thus, he needs to add 1 litre of paint.

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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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04 Jul 2018, 02:09
Bunuel wrote:
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

Hi Bunuel ,

Instead of using part to part , I am using part to whole , approach, why am I not getting the answer !

$$\frac{paint }{ Total \hspace{1mm}quantity}$$=$$\frac{2}{3.5}$$ -> Required ratio
Finally after adding x liters of paint to 3 liters of paint already present the ratio of paint to total mixture is $$\frac{3+x}{6}$$

Hence equating the proportions $$\frac{2}{3.5}=\frac{3+x}{6}$$

x = $$\frac{3}{7}$$

Whys is x not coming to 1?
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Joined: 16 Oct 2010
Posts: 8550
Location: Pune, India
Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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05 Jul 2018, 22:19
1
stne wrote:
Bunuel wrote:
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

Hi Bunuel ,

Instead of using part to part , I am using part to whole , approach, why am I not getting the answer !

$$\frac{paint }{ Total \hspace{1mm}quantity}$$=$$\frac{2}{3.5}$$ -> Required ratio
Finally after adding x liters of paint to 3 liters of paint already present the ratio of paint to total mixture is $$\frac{3+x}{6}$$

Hence equating the proportions $$\frac{2}{3.5}=\frac{3+x}{6}$$

x = $$\frac{3}{7}$$

Whys is x not coming to 1?

Because once you add x litres of paint to the mix, the total mix becomes 6 + x litres.
Hence,

$$\frac{2}{3.5}=\frac{3+x}{6+x}$$
x = 1
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Joined: 27 May 2012
Posts: 611
Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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07 Jul 2018, 10:07
VeritasPrepKarishma wrote:
stne wrote:
Bunuel wrote:
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint

Hi Bunuel ,

Instead of using part to part , I am using part to whole , approach, why am I not getting the answer !

$$\frac{paint }{ Total \hspace{1mm}quantity}$$=$$\frac{2}{3.5}$$ -> Required ratio
Finally after adding x liters of paint to 3 liters of paint already present the ratio of paint to total mixture is $$\frac{3+x}{6}$$

Hence equating the proportions $$\frac{2}{3.5}=\frac{3+x}{6}$$

x = $$\frac{3}{7}$$

Whys is x not coming to 1?

Because once you add x litres of paint to the mix, the total mix becomes 6 + x litres.
Hence,

$$\frac{2}{3.5}=\frac{3+x}{6+x}$$
x = 1

Thank you Karishma.
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- Stne

Manager
Joined: 01 Feb 2018
Posts: 95
Location: India
Schools: ISB '20, NUS '21, NTU '20
GMAT 1: 700 Q47 V38
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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat  [#permalink]

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04 Sep 2018, 22:39
Paint and water need to be in the ratio 2 : 1.5 which is nothing but 4 : 3.
Now 6 L solution has equal amounts of paint and water ( 3 L and 3 L) and we need to bring it to the ratio 4 : 3 (P : W).
Currently W is already 3 L, so if we add another 1 L of paint to the 6 L solution, the new ratio will become 4 : 3 as we require.

Hence Answer is A - 1 L of paint.
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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat &nbs [#permalink] 04 Sep 2018, 22:39
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# Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat

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