Rakesh purchased 4 bats and 10 balls for 3,650. He sold all the bats at the profit of 30% and balls at a loss
of 20%. If his overall profit is 470, what was the cost price of one bat?
Answers
Answer:
your answer is 1030
Step-by-step explanation:
because if we will add 470 to 3,650 we will get 4120 and we will divide 4120÷4 = 1030
The price of 1 bat is Rs. 600.
Given,
The cost of 4 bats and 10 balls = Rs. 3650
Profit in bat = 30%
Loss in ball = 20%
Overall profit = Rs. 470
To Find,
The cost of the bat =?
Solution,
Let the cost price of 1 bat be a and 1 ball be b
4a + 10b = 3650 ⇒ Equation 1
According to the question,
Profit in 1 bat = 30% of the cost of the bat
Profit in 1 bat = 30% of a
Profit in 1 bat = (30/100) x a
Profit in 1 bat = 0.3a
Profit in 4 bats = 4 x 0.3a
Profit in 4 bats = 1.2a
Similarly, Loss in 1 ball = 20% of cost of the ball
Loss in 1 ball = 0.2b
Loss in 10 balls = 10 x 0.2b
Loss in 10 balls = 2b
The overall profit = 470
1.2a - 2b = 470 ⇒ Equation 2
Multiplying equation 2 by 5 and adding it to equation 1, we get
4a + 10b + 5(1.2a - 2b) = 3650 + (5 x 470)
4a + 10b + 6a - 10b = 3650 + 2350
10a + 0b = 6000
a = 6000 / 10
a = 600
The cost price of 1 bat is Rs. 600
Putting value of a in equation 1,
4 x 600 + 10b = 3650
10b = 3650 - 2400
10b = 1250
b = 1250 / 10
b = 125
The cost price of 1 ball is Rs. 125
Hence, the the cost price of one bat is Rs. 600.