Question

There are two varieties of tea worth Rs.90 per
kg and Rs.70 per kg. If X kg of 1st kind is
mixed with 56 kg of 2nd kind to get a profit
25% by selling the mixture at Rs.95 per kg
then X equals to:​

Answer 1

Step-by-step explanation:

x kg of 90 and 56 kg of 70 is mixed then the average price

= x×90 + 56×70 /(x+56) = cp

sp = 95, profit = 25%,

profit = sp-cp/cp ×100

25 = 95 - cp/ cp ×100

0.25×cp = 95- cp

cp(1+.25) =95

cp = 95/1.25 = 76

apply alligation

90 70

76

76-70 90-76

=6 = 14

6:14 = 3:7

90rs is 3x kgs

70rs is 7x kgs

but 7x = 56

x = 56/7 =8

3x = 3×8 =24

weight of 90rs worth tea in the mixture = 24

Answer 2

Answer:

X = 24

Step-by-step explanation:

Recall the formula

Profit % = $\frac{Profit}{Cost \ Price} X100$

Profit = Selling Price - Cost Price

Solution:

Cost of the first variety of tea = Rs.90

Cost of the second variety of tea = Rs. 70

Cost of Xkg of the first variety of tea = 90X

Cost of 56Kg of the second variety of tea = 56×70 = 3920

Total cost of Xkg of first variety and 56kg of second variety = 90X+3920

Total weight of the tea = X+56

Cost per kg = $\frac{90X+3920}{X+56}$

So we have,

Cost Price = CP =   $\frac{90X+3920}{X+56}$ -----------(1)

Selling Price = SP = 95

Profit % = 25%

Profit = SP - SP = 95 -CP

Profit % = $\frac{95 -CP}{CP}$ ×100

25 =  $\frac{95 -CP}{CP}$ ×100

25CP = (95-CP)×100

25CP = 9500-100CP

125CP = 9500

CP = $\frac{9500}{125}$

CP =76 --------------(2)

Comparing Equations(1) and (2) we get

 $\frac{90X+3920}{X+56}$ = 76

90X +3920 = 76(X+56)

90X +3920 = 76X+4256

90X - 76X = 4256 -3920

14X = 336

X = 24

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