Two mixtures of clay and sand contain 40% and 70% sand by weight. When

Question

Two mixtures of clay and sand contain 40% and 70% sand by weight. When both the mixtures are mixed, the resultant mixture is 700 gm. If the resultant mixture contains 45% clay by weight, then what is weight of the first mixture?

A) 254.5 gm
B) 300 gm
C) 350 gm
D) 445.5 gm
E) 583.3 gm

A) 254.5 gm
B) 300 gm
C) 350 gm
D) 445.5 gm
E) 583.3 gm

fauji · Accepted Answer

Approach:

Assume
Mixture 1 be x
Mixture 2 be y

Sand in x - 40%
Sand in y - 70%
Sand after mixing both - 55% (Given -45% Clay)

Using Weighted Average formula:

\frac{.40(x) + .70(y)}{x+y}  = .55

After solving, x:y => 1:1

Given total weight 700 gms - 350 gm each is the answer

Option C

aniruddhap · Answer

Let, the weight of first mixture be x (40% sand), and the weight of second mixture be y (70% sand).

Total mixture has 45% clay thus 55% Sand. Which is average of 40% and 70%. Hence, both the mixtures should have equal weight.

Total = 700, hence each mixture should be of 350gm.

Hence, C.

OR OR OR

Given condition states that, 
Addition of x and y gives 700gm of mixture, which consists of 45% clay. Thus, 55% of Sand.

Eqn 1: x+y=70

Eqn 2: weighted average of sand.

40x + 70y = 55(x+y)
40x + 70y = 55(700)

To find: X ?

Multiple Eqn 1 by 70, Subtracting eqn 2 from it

70x + 70y = 70(700)
-(40x + 70y = 55(700))
 ----------------------
 30x = 15(700)
 x = 350

Hence,C .

Posted from my mobile device

Aadi01 · Answer

What mistake am I doing...can someone tell me

gracie · Answer

let x=weight of first mixture
.4x+.7(700-x)=(1-.45)*700→
x=350 gm
C

CAMANISHPARMAR · Answer

You may do everything correctly in this question and still get the question wrong if you don't read the question carefully. While answering GMAT questions always check whether or not you are answering the right question or not?

aniruddhap · Answer

One prominent mistake that can be spotted is, Clay % of M2 should be 30 and not 40.

Give it a try now.

If not, try to adopt a better approach stated above

Posted from my mobile device

ScottTargetTestPrep · Answer

Solution:
 
If the first mixture contains 40% sand, then it contains 60% clay. Similarly, if the second mixture contains 70% sand, then it contains 30% clay. Since the resultant 700-gram mixture contains 45% clay and 45% is exactly the average of 60% and 30%, we must have an equal amount (in weight) of the first mixture and second mixture. Therefore, the weight of the first mixture is 700/2 = 350 grams.

Answer: C

Nehakumari3107 · Answer

Can anyone please post the answer by the diagram method or cross method

MBAchild · Answer

This question can be made little more interesting by asking "What is the amount of clay in the new mixture that came from the first mixture" ?

saynchalk · Answer

Focus on the clay

Divyanshu14 · Answer

Clay should be 30% in M2

ravi1522 · Answer

Hello ,
As the mixture have clay and sand 
40% sand and 70% sand 
then clay will be 60% and 30%

when mix together it is 45%
so if you observe if take average of 60% and 30% it gives 45% that means the both mixture is mix in 1:1 ratio
so total weight is 700 gm ,so each will be 350Gm each

Hence option C is correct

Thanks .

Two mixtures of clay and sand contain 40% and 70% sand by weight. When

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Two mixtures of clay and sand contain 40% and 70% sand by weight. When

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