A lump of two metals weighing 18 gms. is worth Rs.87 but if their weight be interchanged, it would b

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22 Jun 2016 Mixture

A lump of two metals weighing 18 gms. is worth Rs.87 but if their weight be interchanged, it would be worth Rs.78.60. If the price of one metal be Rs.6.70 per gm., find the weight of the other metal in the mixture.

OPtion

1) 5 gm
2) 4 gm
3) 8 gm
4) 6 gm
5) 14 gm
6) 12 gm
7) 7 gm
8) 10 gm
9) 9 gm
10)None of these

Solution

If one lump is mixed with another lump with the quantities of metals interchanged then the mixture of the two lumps would contain 18 gm. of first metal and 18 gm. of second metal and the price of the mixture would be Rs. (87+78.60) or Rs. 165.60
=> Cost of (18 gm of 1st metal + 18 gm of 2nd metal)
= Rs. 168.60
So cost of (1 gm of 1st metal + 1 gm of 2nd metal)
= Rs. 165.60/18 = Rs. 9.20
Now mean price of lump = Rs. (87/18) per gm = Rs. (29/6)
By alligation rule
Quantity of 1st metal/Quantity of 2nd metal = 14/6 : 56/30 = 5:4
In 9 gm of mix, 2nd metal = 4 gm
In 18 gm of mix 2nd metal = 4/9 *18 = 8 gm
Option 3)

Correct Option: 3 Best Solution (11)

ANUJ KUMAR   8 years AGO

let x is wt of first metal
p be price of other metal per gm

6.7*x + p(18-x)=87
6.7*(18-x)+ p*x=78.60

Solving we get x=10
so wt of other metal is 18-x =>8gms

Like? Yes (10) | No   

RAVAL   8 years AGO

suppaose A is x gms
then B is (18-x) gms.
so. equation is like to be
Ax+B(18-x) =87
A(18-x)+Bx =78.6
soving both equation
we get B is 8 gms & A is 10 gms
ans. 8 gms....

Like? Yes (4) | No (1)  

Kumar Navendu   8 years AGO

6.7x +(18-x)y = 78.6 ----------1

6.7(18-x) + xy = 87 ----------- 2

=>6.7x - 33.6 = xy ------------------3
=>6.7x + 18y - 78.6 = xy -----------4

solving 3 and 4
y=2.5

put value of y in equation 3
x = 8

Like? Yes (3) | No (1)  

Shafigheh Nikpour   8 years AGO

price of one metal per gram=6.7
price of second metal per gram=p
weight of one metal in mixture=x
weight of second metal in mixture=18-x
before interchange: 6.7*x+p(18-x)=87
after interchange:6.7(18-x)+px=78.6
after solving: p=2.5 ,x=10
so weight of second metal in mixture=8
option 3

Like? Yes (2) | No   

RAHUL KUMAR   8 years AGO

Cost of (18 g of 1 metal + 18 g of 2 metal) = Rs. 165.60

Cost of (1 g of 1 metal + 1 g metal of 2 metal) = Rs. 9.20

Hence cost of 1 g of 2nd metal,
= 9.20 - 6.70 = Rs. 2.5

Mean price = Rs. 87/18

6.7. 2.5

87/18

14/6. 56/30

Now, quantity of 1 metal /quantity of 2 metal = 14/6:56/30 = 5:4

Quantity of 2nd metal = (18*4)/9 = 8 g.

option (3)

Like? Yes (1) | No   

medha rawat   8 years AGO

let x,y be quanties and p,q cost
x+y=18
xp+(18-x)q=87
xq+(18-x)p=78.6
x=10
y=8

Like? Yes (2) | No (1)  

Divesh Singla   8 years AGO

Cost of (18 g of 1st metal + 18 g of 2nd metal) = Rs. 165.60
Cost of (1 g of 1st metal + 1 g metal of 2nd metal) = Rs. 9.20
Hence cost of 1 g of 2nd metal,
= 9.20 - 6.70
= Rs. 2.5
Mean price = Rs. 87/18

Now, quantity of 1st metal /quantity of 2nd metal = 14/6:56/30 = 5:4
Quantity of 2nd metal = (18*4)/9 = 8 g.

Like? Yes (1) | No   

Jayakumar J N   8 years AGO

Made 3 equations from the question. Solved for 1 variable. Answer is 8 gm.

Like? Yes | No   

Mukund Manohar   8 years AGO

Cost of (18g of 1st metal + 18g of 2nd metal) = Rs 165.60
Cost of(1g of !st metal + 1g of 2nd metal) = (165.60/18)
= Rs 9.20
So,Cost of 1g of 2nd metal = 9.20 - 6.70
= Rs 2.50
Now, Mean Price of the mixture per gram = Rs 87/18
By the alligation rule,two metals are in the ratio of 5:4
Weight of 2nd metal = (18*4)/9 = 8 gm

Like? Yes | No (1)  

Lakshmipathi   8 years AGO

given condition is x+y=18;
assume x=10,y=8;
10(6.70)+8(?)=87
67+8(?)=87
?=2.5
10(2.5)+8(6.70)=78.6
25+53.60=78.6
78.60=78.60;
we need another metal weight 8 gms

Like? Yes | No (1)  

Manikanta Nandam   8 years AGO

if one metal is x, another metal is 18-x
x metal cost is 6.70 per gr
y metal cost is y(say)
then
x(6.70)+(18-x)y=87----(1)
after interchanging
(18-x)(6.70)+xy=78.60----(2)
2 equations 2 unknowns by solving this we get x=10
but another metal weight is (18-10)=8grms

Like? Yes | No (1)