Question

Tue ratio of the prices of tea last year and this year is 5:6. The ratio of the prices of coffer last year amd this year is 7:8. The sum of prices of a kg of tea and a kg of coffee this year is ₹48. Find the price of tea (in ₹) last year if it was 20/21 of the price of coffee last year.

Answer 1

Answer:

Last year tea price was Rs 20/-

Answer 2

The price of tea in last year is ₹20.

Explanation:

Given : The ratio of the prices of tea last year and this year is 5:6.

The ratio of the prices of coffer last year and this year is 7:8.

Let the price of a kg of tea last year be 5x and this year be 6x.

Let the price of a kg of coffee last year be 7y and this year be 8y.

Since , the sum of prices of a kg of tea and a kg of coffee this year is ₹48.

$\Rightarrow\ 6x+8y=48\\\\\Rightarrow\ 3x+4y=24-------(1)$

Also, the price of tea (in ₹) last year if it was 20/21 of the price of coffee last year.

$5x=\dfrac{20}{21}\times7y\\\\\Rightarrow\ x=\dfrac{20}{3\times5}y=\dfrac{4}{3}y--------(2)$

Substitute the value of x in (1) , we gte

$3(\dfrac{4}{3}y)+4y=24\\\\\Rightarrow\ 4y+4y=24\\\\\Rightarrow\ 8y=24\\\\\Rightarrow\ y=3$

Put value of y in (2) , we get

$x=\dfrac{4}{3}\times3=4$

Then, the price of tea last year = 5x =5(4)= Rs 20

Hence, the price of tea in last year is ₹20.

# Learn more :

The prices of two radios are in the ratio x:y

When the prices are both increased by £20, the ratio becomes 5:2

When the prices are both reduced by £5, the ratio becomes 5:1

Express the ratio x:y in its lowest terms.

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