A tea merchant blends two varieties of tea costing her Rs 234 and Rs 130 per kg in the ratio of their costs. If the weight of the mixture is 84kg, then find the weight of each variety of tea.

Question

Philoid · Accepted Answer

Let the two varieties of tea be ‘A’ and ‘B’

Cost of ‘A’ = 234 Rs

Cost of ‘B’ = 130 Rs

Ratio of their costs = =

Divide numerator and denominator by 2

⇒ Ratio of their costs =

Divide numerator and denominator by 13

⇒ Ratio of their costs = …(i)

Weight of mixture = 84 kg

Let the weight of type ‘A’ tea in the mixture be ‘a’ and as total is 84 the weight of type ‘B’ tea would be (84 – a)

Now given that the ratio of two varieties of tea in the mixture is same as the ratio of their costs

Using (i) and given condition

⇒ =

Cross multiply

⇒ 9 × (84 – a) = 5a

⇒ 756 – 9a = 5a

⇒ 756 = 14a

⇒ a =

Divide numerator and denominator by 7 we get

⇒ a = = 54 kg

⇒ 84 – a = 84 – 54 = 30 kg

Therefore, weight of 234 Rs/kg tea in mixture is 54 kg and weight of 130 Rs/kg tea in mixture is 30 kg