Profit and Loss

Given
Cost price (C.P) of 40 dozen of bananas is equal to selling (S.P) of 25 dozen of bananas.
Let the C.P of 1 dozen of banana = ₹1
Therefore C.P of 25 dozen bananas = ₹ 25
and C.P of 40 dozen bananas = ₹40
⇒ C.P of 40 dozen of bananas = S.P of 25 dozen bananas = ₹40
Profit % = (S.P of 25 dozen bananas - C.P of 25 dozen bananas) / C.P of 25 dozen bananas × 100%
= {(40 - 25) / 25} × 100%
= {15 / 25} × 100%
= 60%
∴ required Profit % = 60 %

Let the cost price of each pencil be ₹ k
We have, S.P of 100 pencils = C.P of 120 pencils = 120k
We know that C.P of 100 pencils = 100 k
Gain on the purchase of 100 pencils = S.P - C.P
⇒ Gain = 120 k - 100 k =20k
Profit percentage = (profit/C.P)×100 = (20k/100k)×100 = 20%

Profit rate of R = 10%
Profit rate of R = 1/3 of profit rate of Q
10 = 1/3 of Q
Q = 30%
Profit rate of P = 5/3 of profit rate of Q
= (5/3)×30
P = 50%
Cost price of S is the selling price of R
SP of R = ₹ 2145
CP = SP×[100/(100 + profit)]
CP of R = 2145×[100/(100 + 10 )]
= 2145×(100/110)
=₹ 1950
∴ the cost price of R is selling price of Q.
So, CP of Q = 1950×[100/(100 + 30)]
= 1950×(100/130)
= ₹ 1500
Therefore the cost price of Q is the selling price of P.
So, CP of P = 1500×[100/(100 + 50)]
= 1500×(100/150)
CP of P = ₹ 1000.

Let cost price of sofa be = ₹ x.
SP = [(100 + Gain)/100]×CP
SP = [(100 + 20)/100]×x
SP = (120/100)x
SP = 6x/5
we know that,
(SP - 100) = (CP -100) × [(100 + Gain)/100]
[(6x/5) - 100] = (x - 100) × [(100 + 20)/100]
[(6x/5) - 100] = (x - 100) × (125/100)
[(6x/5) - 100] = (x - 100)×(5/4)
(6x/5) - (5x/4) = (100/4) - (500/4)
-(x/20) = - 25
x = ₹ 500.

We know that the clock was sold at loss of 25% it means that only 75% of the cost price is paid.
Which means, 75% of C.P = 480
⇒ (75/100)×C.P = 480
⇒ C.P = 480×4/3
= 160×4
= 640 ₹
Cost price of an clock = ₹ 640

Suppose he bought 5 kg and 3 kg of tea.
Cost Price = ₹ (5×18 + 3×20) = ₹ 150.
Selling price = ₹ (8×21) = ₹ 168.
Profit = 168 - 150 = 18
So, Profit % = (18/150) × 100 = 12%

S.P = 26000 and C.P = 24700.
Profit = S.P – C.P = 26000 – 24700 = 1300
Profit percentage = (Profit /C.P)×100 = (1300/26000)×100 = 100 / 20 = 5 %

Price reduced in percentage = 20 %
Reduced price of potato be =(30 / 2)×(20 / 100) = 3 ₹ per kg

Cost of the onion be 1 Re per kg.
He sells for Re 1 what cost to him is ₹ 0.96
Gain = 1 – 0.96 = 0.04
Gain percentage = (0.04/0.96)×100 = 25/6 %

Let the cost price be ₹ k
Now, We got from Q, 600 – k = k – 400 ⇒ 2k = 1000 ⇒ k = 500
Again, selling price of the nightstand for making 25 % profit = (500×125) /200 = ₹ 625