20kg of rice costing ₹80 per kg is mixed with ykg of rice costing ₹100 per kg. If the cost of this mixed rice is ₹84 per kg, what is the value of y?
- A6
- B3
- C4
- D5
Solution & Step-by-step Explanation
We can use the rule of alligation or weighted average to solve this problem.
Using the weighted average equation:
Average Price=
w
1
+w
2
P
1
⋅w
1
+P
2
⋅w
2
Substitute the given values:
P
1
=80, w
1
=20
P
2
=100, w
2
=y
Average Price=84
84=
20+y
80×20+100×y
84(20+y)=1600+100y
1680+84y=1600+100y
1680−1600=100y−84y
80=16y
y=
16
80
=5
Therefore, the value of y is 5.
Using the weighted average equation:
Average Price=
w
1
+w
2
P
1
⋅w
1
+P
2
⋅w
2
Substitute the given values:
P
1
=80, w
1
=20
P
2
=100, w
2
=y
Average Price=84
84=
20+y
80×20+100×y
84(20+y)=1600+100y
1680+84y=1600+100y
1680−1600=100y−84y
80=16y
y=
16
80
=5
Therefore, the value of y is 5.