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

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New post 16 May 2016, 02:46
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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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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat [#permalink]

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New post 16 May 2016, 02:58
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

Answer : A
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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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New post 16 May 2016, 03:04
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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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New post 25 May 2017, 11:12
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

Hence A answer
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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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New post Updated on: 04 Jul 2018, 11:12
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, 11:29.
Last edited by gracie on 04 Jul 2018, 11:12, 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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New post 31 May 2017, 19:03
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.

Answer: 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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New post 04 Jul 2018, 03:09
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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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat [#permalink]

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New post 05 Jul 2018, 23:19
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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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat [#permalink]

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New post 07 Jul 2018, 11:07
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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Re: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts wat   [#permalink] 07 Jul 2018, 11:07
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