A restaurant makes its regular sauce from 5 parts sweet sauce and 3

Question

A restaurant makes its regular sauce from 5 parts sweet sauce and 3 parts chilli sauce. Then its spicy sauce is made from 5 parts chilli sauce and 3 parts sweet sauce. How many cups of chilli sauce must be mixed with a 24-cup regular sauce to turn it to spicy sauce?

A) 6
B) 12
C) 16
D) 24
E) 30

A) 6
B) 12
C) 16
D) 24
E) 30

chetan2u · Accepted Answer

Hi,

24 cup regular sauce... 
Total parts 3 chilli + 5 sweet = 8 parts..
Here each part =  \frac{24}{8}=3 ..
Chilli - 3*3=9 and sweet - 3*5=15

Since ONLY chilli sauce is added, we can keep sweet to be constant 
Sweet=15 cups..
Now sweet becomes 3 parts out of 3+5 or 8 parts.
So  \frac{3}{8}*T=15......T=\frac{15*8}{3}=40 ..
Total becomes 40 from 24 and all added is chilli..
So cups of chilli sauce added=40-24=16

C

gracie · Answer

let x=cups of chilli sauce to be mixed
3/8*24+x=5/8*(24+x)
x=16
C

amathews · Answer

chetan2u, did it take you under 1.5 mins to do this question? If so, any tips? Takes me 2+ mins to do these type of mixture conversion questions.

chetan2u · Answer

Hi amathews,

It took exactly 10 secs more than reading the Q as I could solve it in mind.
But that may be because I am ok at these things. I would have thought of some other way if it would not have come this way.

How you can do it?
If you are able to make up for the extra time in mixture Q in some other topics, it may well be fine as it is.
But if not then you can improve speed by practicing and learning new methods and see what suits you. Each Q requires a different approach depending on what is given. I am sure you too can get a hang of it with practice.

amathews · Answer

Ty for your advice in the matter

rkoberoi · Answer

Regular Sauce = 24 cups 
3/8 are chilli =  9 cups

Let x=cups of chilli sauce to be mixed
as it is chilli so all cups are chilli =  x cups

total cups = 24+x 
Chilli in total is  5/8(24+x)

Chilli in regular sauce + Chilli in chilli sauce = Chilli in new sauce 
9+x = 5/8(24+x)
3x=48
x=16

satya2029 · Answer

Regular sauce=sweet sauce/ chilli sauce=5/3
24 Cups of regular sauce will give (15 parts sweet sauce AND 9 parts chilli sauce)
Spicy sauce=chilli sauce/sweet sauce=5/3=25/15
So for 15 parts of sweet sauce you need 25 parts of chilli sauce.
Hence you need 16 cups of chilli sauce(25=16+9)
16:)

homersimpsons · Answer

VeritasKarishma  how do we solve this question using weighted average

minustark · Answer

In a 24-cup regular sauce, there are 5/8 *24 = 15 cups of sweet sauce and 9 cups of chili sauce. We have to make 15 cups of of sweet sauce 3/8 part of the spicy sauce, so the total sauce will be of 40 cups. the remaining 25 cups are chili sauce.

So, new chili sauce added = 25 - 9 = 16 cups

C is the answer.

KarishmaB · Answer

Regular sauce is 3/8 chilli (A1)
Chilli sauce is 1 chilli (A2)

Spicy sauce is 5/8 chilli (Aavg)

We need to add w cups of chilli sauce (w2) to 24 cups of regular sauce (w1) to make spicy sauce.

24/w = (1 - 5/8) / (5/8 - 3/8) 
w = 16 cups

Answer (C)

ThatDudeKnows · Answer

24 cups of regular sauce has 15 cups sweet and 9 cups chilli.

We want to have 5 cups chilli for every 3 cups sweet. We have 15 cups sweet, so we need 25 cups chilli.

We already have 9 cups chilli and need 25 cups, so we need to add 16 cups.

Answer choice C.

youcouldsailaway · Answer

After adding x amt of a particular ingredient to a sauce S, the proportion of that ingredient C, changes in the total proportional mix, T.

\frac{T }{ T}  = 1 whole quantity of S, whatever the S may be]

In terms of an equation,

\frac{Old C}{T}  * S + x =  \frac{New C }{ T}  * (S + x)

Therefore,

( \frac{3 }{ 8}  * 24) + x =  \frac{5}{8}  * (24 + x)

X = 16

Paras96 · Answer

A restaurant makes its regular sauce from 5 parts sweet sauce and 3 parts chilli sauce. Then its spicy sauce is made from 5 parts chilli sauce and 3 parts sweet sauce. How many cups of chilli sauce must be mixed with a 24-cup regular sauce to turn it to spicy sauce?

A) 6
B) 12
C) 16
D) 24
E) 30

No. of cups of sweet sauce in 24-cup regular sauce = 5*24/8 = 15
No. of cups of chilli sauce in 24-cup regular sauce = 3*24/8 = 9

Let the no. of cups of chilli sauce to be added in 24-cup regular sauce to turn it to spicy sauce =x

Since Ratio of chilli sauce to sweet sauce for spicy sauce = 5:3

Therefore, here => (9+x)/15 = 5/3
=>9 + x = 25
=>x=16

Hence C

luisdicampo · Answer

Deconstructing the Question

Regular sauce has ratio   5:3   (sweet to chili), and spicy sauce has ratio   3:5  .

We start with   24   cups of regular sauce and add only chili sauce.

We want to reach the spicy ratio.

Step-by-step

Total parts in regular sauce are

5 + 3 = 8

Sweet is

\frac{5}{8} \cdot 24 = 15

Chili is

\frac{3}{8} \cdot 24 = 9

Let added chili be

x

Then chili becomes

9 + x

Sweet remains

15

We want

\frac{15}{9 + x} = \frac{3}{5}

Solve:

15 \cdot 5 = 3(9 + x)

75 = 27 + 3x

48 = 3x

x = 16

Answer: C

A restaurant makes its regular sauce from 5 parts sweet sauce and 3

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A restaurant makes its regular sauce from 5 parts sweet sauce and 3

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