Question

One kilogram of tea and 4 kg of sugar together cost Rs220. If the price of sugar increases by 50% and the price of tea increases by 10%,the cost would be Rs226.Find the original cost per kilogram each.

Answer 1

x+4y=220
(x+10x/100) +4(y+50y/100)=266=> 11x+60y=2660. (eq.1)
11(x+4y)=11*220=> 11x+44y=2420. ( eq.2 )

Now eq. 1 - eq.2

y=15
x=220-4y
x=160

Answer 2

Answer:

The cost of tea per kg be Rs 160 and the cost of sugar per kg be Rs 15.

Solution:

Assume the cost of tea be x

Let us assume that the cost of sugar be y

Given that

$\mathrm { x } + 4 \mathrm { y } = 220 \ldots ( 1 )$

After the increase of sugar price by 50% and the tea price by 10%, the equation will be

$\begin{array} { c } { \left( x + \frac { 10 x } { 100 } \right) + 4 \left( y + \frac { 50 y } { 100 } \right) = 266 } \\\\ { 11 x + 60 y = 2660 \ldots ( 2 ) } \end{array}$

Multiply the equation (1) × 11

$11 \mathrm { x } + 44 \mathrm { y } = 2420 \ldots ( 3 )$

Subtract the equation (2) from (3)

$\begin{array} { c } { 11 \mathrm { x } + 60 \mathrm { y } = 2660 } \\\\ { 11 \mathrm { x } + 44 \mathrm { y } = 2420 } \\\\ { 60 \mathrm { y } - 44 \mathrm { y } = 2660 - 2420 } \\\\ { 16 \mathrm { y } = 240 } \\\\ { \mathrm { y } = 15 } \end{array}$

Substitute the y value in equation (1)

$\begin{array} { c } { x + 4 \times 15 = 220 } \\\\ { x + 60 = 220 } \\\\ { x = 220 - 60 } \\\\ { x = 160 } \end{array}$

Thus, the cost of tea per kg be Rs 160 and the cost of sugar per kg be Rs 15.