A trader sells three motorcycles for Rs 5400, Rs 3300 and Rs 5250 respectively. He gains 20% on the first motorcycle, 10% profit on the second and 25/8% loss on the total. Find the cost price of the third.
Answers
Step-by-step explanation:
Given :-
A trader sells three motorcycles for Rs 5400, Rs 3300 and Rs 5250 respectively. He gains 20% on the first motorcycle, 10% profit on the second and 25/8% loss on the total.
To find :-
Find the cost price of the third ?
Solution :-
The Selling Price of the first motorcycle
= Rs. 5400
Profit on it = 20%
We know that
Cost price = (100×SP)/(100+g)
=> CP = (100×5400)/(100+20)
=> CP = 540000/120
=> CP = 54000/12
=> CP = 4500
Cost price of the first motorcycle
= Rs. 4500
The selling price of the second motor cycle = Rs. 3300
Profit on it = 10%
We know that
Cost price = (100×SP)/(100+g)
=> CP = (100×3300)/(100+10)
=> CP = 330000/110
=> CP = 33000/11
=> CP = 3000
Cost price of the second motorcycle
= Rs.3300
The Selling Price of the third motorcycle
= Rs. 5250
Let the cost price of the third motorcycle be Rs. X
Total Selling prices of the three motorcycles = 5400+3300+5250
=> Rs. 13950
Total Cost prices of the three motorcycles = 4500+3000+X
=> Rs. (7500+X)
Given that
Loss on the whole translation = 25/8%
So, It is clear that
CP > SP
We know that
Cost price = (100×SP)/(100-l)
=> 7500+X = (100×13950)/[100-(25/8)]
=> 7500+X = 1395000/[(800-25)/8]
=> 7500+X = 1395000/(775/8)
=> 7500+X = (1395000×8)/775
=> 7500+X = 11160000/775
=> 7500+X = 14400
=> X = 14400-7500
=> X = 6900
Therefore, The Cost of the third motorcycle = Rs. 6900
Answer:-
The Cost Price of the third motorcycle is
Rs. 6900
Check :-
CP of three motorcycles
= Rs. 4500+3000+6900
=> 14400
SP of the three motorcycles = Rs. 13950
As we know ,Loss = CP-SP
=> Loss = 14400-13950
=> Loss = Rs. 450
Loss % = (Loss/CP)×100
=> Loss% = (450/14400)×100
=> Loss% = 450/144
=> Loss% = (25×18)/(8×18)
=> Loss% = 25/8
We get Loss% as 25/8% which is given in the problem.
Verified the given relations in the given problem.
Used formulae:-
→ Cost price = (100×SP)/(100+g)
→ CP = (100×SP)/(100-l)
→ Loss = Cost Price - Selling Price
→Loss % = (Loss/CP)×100
- CP = Cost Price
- SP = Selling Price
- g = gain or profit
- l = loss