Question

20
The cost of 15 kg tea and 17 kg coffee is Rs. 183 and the cost of 25 kg tea and 13
re coffee is Rs. 213. What will be the cost of7 kg tea and I kg coffee?
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Answer 1

Correct Question :-

The cost of 15 kg tea and 17 kg coffee is Rs 183 and the cost of 25 kg tea and 13kg coffee is Rs 213. What will be the cost of 7 kg tea and 1 kg coffee ?

Given data :-

• The cost of 15 kg tea and 17 kg coffee is Rs 183.
• The cost of 25 kg tea and 13 kg coffee is Rs 213.

Solution :-

Let, the cost of one kg tea be x and the cost of one kg coffee be y.

Now, {from given}

→ 15x + 17y = 183 ......( 1 )

→ 25x + 13y = 213 ......( 2 )

Multiply eq. ( 1 ) by 25, we get

→ 375x + 425y = 4575 .....( 3 )

Multiply eq. ( 2 ) by 15, we get

→ 375x + 195y = 3195 ......( 4 )

Now, subtract eq. ( 4 ) from eq. ( 3 )

375x + 425y = 4575

- ( 375x + 195y = 3195 )

______________________

230y = 1380

y = 1380/230

y = 6

Hence, cost of one kg coffee is Rs 6

Now, put value of y in eq ( 1 )

→ 15x + 17y = 183

→ 15x + 17( 6 ) = 183

→ 15x + 102 = 183

→ 15x = 183 - 102

→ 15x = 81

→ x = 81/15

→ x = 27/5

→ x = 5.4

Hence, the cost of one kg tea is Rs 5.4

Now to find the cost of 7 kg tea

→ cost of 7 kg tea = 7 × {cost of one kg tea}

→ cost of 7 kg tea = 7 × 5.4

→ cost of 7 kg tea = Rs 37.8

Hence, the cost of 7 kg tea is Rs 37.8 and the cost of one kg coffee is Rs 6 .