One kilogram of tea and 4 kg of sugar together cost Rs.220. If the price of sugar increases by 50% and the price of tea increases by 10% the cost would be Rs.266. Find the original cost per kilogram of each.

A
$Rs . 60, Rs . 40$
B
$Rs . 60, Rs . 30$
C
$Rs . 60, Rs . 20$
D
$Rs . 20, Rs . 40$

Solution:

Given that 1 kg of tea and 4 kg of sugar together cost Rs. 220.
If the price of sugar increases by 50% and price of tea increases by 10% the cost would be Rs. 266.
Let the cost price of the tea and sugar be

x

and

y

respectively.
Since, 1 kg of tea and 4 kg of sugar together cost Rs. 220, thus,

\Rightarrow x + 4 y = 220

……..(1)
Since, the price of sugar increases by 50% and price of tea increases by 10% the cost would be Rs. 266. Thus,

\Rightarrow [x + (\frac{50}{100} x)] + 4 [y + (\frac{10}{100} y)] = 266

\Rightarrow \frac{3}{2} x + 4 (\frac{11}{10} y) = 266

\Rightarrow \frac{3}{2} x + \frac{22}{5} y = 266

……………(2)
Multiply equation (1) by

\frac{3}{2}

and then subtract equation by (2), we get,

\Rightarrow \frac{3}{2} x + 6 y - \frac{3}{2} x - \frac{22}{5} y = 330 - 266

\Rightarrow (\frac{30 - 22}{5}) y = 64

\Rightarrow \frac{8}{5} y = 64

\Rightarrow y = 40

Substituting y=40 in equation (1),

\Rightarrow x + 4 (40) = 220

\Rightarrow x + 160 = 220

\Rightarrow x = 60

Therefore, the cost prices of tea and sugar is

Rs . 60

and

Rs . 40

per kilogram, respectively.
Hence the correct option is 1.

One kilogram of tea and $4 kg$ of sugar together cost Rs.220. If the price of sugar increases by $50 %$ and the price of tea increases by $10 %$ the cost would be Rs.266. Find the original cost per kilogram of each.

Solution:

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