Question

the cost of 5 kg sugar and 7 kg of rice is rupees 153 and the cost of 7 kg sugar and 5 kg rice is rupees 147 find the cost of 1kg of both rice and sugar

Answer 1

Let the cost of 1 kg of sugar be x

And the cost of 1 kg of rice be y

5x + 7y = 153 ------------- [ 1 ]

7x + 5y = 147 ------------- [ 2 ]

[ 1 ] x 7 : 35x + 49y = 1071 ------------- [ 1a ]

[2] x 5 : 35x + 25y = 735  ------------- [ 2a ]

[1a] - [2a] :

49y - 25y = 1071 - 735

24y = 336

y = 14 ------------- [ sub into [ 1 ] to solve for x ]

5x + 7y = 153

5x + 7(14) = 153

5x + 98 = 153

5x = 55

x = 11

Find the cost of 1 kg of rice and sugar:

Rice = x = Rs 11

Sugar = y = Rs 14

Answer: 1 kg of rice costs Rs 11 and 1 kg of sugar costs Rs 14.

Answer 2

$\bold {\huge {Solutions :-}}$

Suppose the cost of 1 kg of sugar be x

And the cost of 1 kg of rice be y

So,

$\bold {5x + 7y = 153}$ ------------ (i)

$\bold {7x + 5y = 147}$ ----------- (ii)

(ii) $\bold { 7x : 35x + 49y = 1071}$ ----------- (i.a)

(ii) $\bold { 5x : 35x + 25y = 735}$  ------------ (ii.a)

(i.a) - (ii.a)=>>>>

$\bold {=> 49y - 25y = 1071 - 735}$

$\bold {=> 24y = 336}$

$\bold {=> y = 14 }$
--------- [ sub into (i) to solve for x ]

$\bold {=> 5x + 7y = 153 }$

$\bold {=> 5x + 7(14) = 153}$

$\bold {=> 5x + 98 = 153}$

$\bold {=> 5x = 55}$

$\bold {=> x = 11}$

The cost of 1 kg of rice and sugar:

Rice = x = Rs 11

Sugar = y = Rs 14

Hence,
$\bold {Cost ~of~ 1~ kg~ rice ~= ~Rs ~11 }$
$\bold {And}$
$\bold {Cost ~of~ 1~ kg~ sugar~ =~ Rs ~14}$