a shopkeeper plants two varieties of tea costing rupees 100 per kg and rupees 170 per kg in the radio of 5 : 2 if he sells the blooded variety at the rate of rs 140 per kg find his gain or loss percent
Answers
Answer: Let the two types of team be m and n. Cost of m type of tea is Rs 18 per 100 gm and n type of tea is Rs 13 per 100 gm.
Therefore, the cost of 1 gm of m type of tea will be given by 18100 = Rs 0.18.
Similarly, the cost of 1 gm of n type of tea will be given by 13100 = Rs 0.13.
Now, it is given that they are mixed in the ratio of 7 : 3.
If there is 100 gm of tea, then 7k + 3k = 100, where k is a constant.
⇒ 10k = 100
⇒ k = 10
Therefore, in 100 gm, the quantity of m type of tea is 7(10) = 70 gm and the quantity of n type of tea is 3(10) = 30 gm.
Now, the total cost price will be the sum of 70 gm of m type of tea and 30 gm of n type of tea.
⇒ cp = 70 (0.18) + 30 (0.13)
⇒ cp = 12.6 + 3.9
⇒ cp = 16.5
Therefore, the total cost price is Rs 16.5 and the selling price is Rs 18.15.
Hence, the gain will be given as the difference between the selling price and the cost price.
⇒ g = 18.15 – 16.5
⇒ g = 1.65
Now, the total gain percentage will be given as p=gcp×100%, p is percentage gain, g is gain and cp is the cost price.
⇒p=gcp×100%⇒p=1.6516.5×100%⇒p=10%