Question

In what ratio should the Assam tea at 40
per kg and Darjeeling tea at 365 per kg be
mixed and sold at 60 per kg to make an
overall profit of 25% ?​

Answer 1

Answer:

Rs 60/kg the S.P. = 60 * 25 = 1500

Step-by-step explanation:

Let’s say mixed tea of 100kg be sold to make 25% profit at Rs 60/kg

So S.P = 60 * 100 = Rs 6000

Now, let’s say ‘x’ kg of first and ‘y’ kg of second tea to be mixed to achieve the same. So

x + y = 100 …. Eq 1

Also, C.P. of mixed tea = 40x + 65y ….Eq 2

Now, Profit % = (Profit * 100)/ C.P. = (S.P. - C.P.) * 100/C.P ….Eq 3

since we want Profit % = 25%

Eq 3 will become: 25 = [6000 - C.P.] * 100 / C.P.

Now, solve it for C.P

25 C.P. = (6000 - C.P.)*100

C.P. = (6000 - C.P.)*4

C.P. = 24000 - 4C.P>

5 C.P. = 24000

C.P. = 4800

So from Eq 2, we can say that

40x + 65y = 4800 ….Eq 4

Now, solve Eq 1 and e.q 4 for the value of x and y

eq 1 * 40 will be 40x + 40y = 4000 ….eq 5

So eq 4 - eq 5 will be 25y = 800 i.e. y = 32

So from eq 1, x will be 100 - 32 = 68

So the ratio in which first tea to second tea be mixed will be

ratio of x:y i.e. 68:32 = 17:8

Now, let do the answer check:

C.P. of 17 kg of first tea = 17 * 40 = Rs 680

C.P. of 8 kg of second tea = 8 * 65 = Rs 520

So Total C.P. = 680 + 520 = 1200

Now, if we have to make a profit of 25% then it’s S.P. = 1200 * 1.25 = Rs 1500

Now, since we mixed 17 kg and 8 kg of teas respectively, we actually had 17 + 8 = 25 kg of mixed tea and we sell 25 kg of mixed tea @ Rs 60/kg the S.P. = 60 * 25 = 1500.

Hence proved