the cost of 5 kg rice, 2 kg sugar and 5 kg of wheat is Rs 23. The cost of 4kg of rice, 4 kg of sugar and 2 kg of wheat is Rs 19. The cost of 3 kg of rice, 2 kg of sugar and 4 kg of wheat is Rs 18. Find the rate per kh of each of these commodities.
Answers
Answer:
Let rate per kg for rice be x
for sugar be y
for wheat be z
∴ 5x + 2y + 5z = 23 →eq. 1
4x + 4y + 2z = 19 →eq. 2
3x + 2y + 4z = 18 →eq. 3
Subtracting eq.3 from eq.1,
eq.1 - eq.3⇒ 5x + 2y + 5z - 3x - 2y - 4z = 23 - 18
2x + z = 5 →eq. 4
multiplying eq.3 by 2,
6x + 4y + 8z = 36 →eq. 5
Subtracting eq.2 from eq.3,
eq.3 - eq.2⇒ 6x + 4y + 8z - 4x - 4y - 2z = 36 - 19
2x + 6z = 17 →eq. 6
Subtracting eq.4 from eq.6,
eq.6 - eq.4⇒ 2x + 6z - 2x - z = 17-5
5z = 12
z = 2.4
substituting value of z in eq. 4,
2x + 12/5 = 5
10x + 12 = 25
x = 13/10
x = 1.3
substituting value of x and z in eq.1,
5×1.3 + 2y+ 5×12/5 = 23
2y = 23 - 6.5 -12
y = 4.5
∴ rate per kg for rice = Rs 1.3
rate per kg for sugar = Rs 4.5
rate per kg for wheat = Rs 2.4