Word Problems on profit and loss

How to Calculate

Solved Problems :

1. A cycle was purchased for 1600 \$ and sold for 1400 \$ . Find the loss and loss% ?

Solution :

We have ,

Cost Price of the cycle = 1600 \$ ,

Selling price of the cycle = 1400 \$

Since S.P < C.P. So thereis loss given by

Loss = C.P - S.P

⇒ Loss = 1600 \$ - 1400 \$ = 200 \$

Now,

Loss % =[ [Loss/C.P] * 100]% = [ [200/1600] × 100]% = 12½ %

Hence , Loss = 200 \$ and Loss % = 12½ %

2. Randy purchased a radio set for 300 \$ and sold it to sally at a profit of 25% . Sally sold it to Thomas at aloss of 10% . For how much did Thomas buy it ?

Solution:

We have ,

Cost price of the radio set for Randy = 300 \$

Gain = 25% of 300 \$

⇒ Gain = [25/100] × 300 = 75 \$

∴  S.P of the radio set for Randy = C.P + Gain

= 300 \$ + 75 \$ = 375 \$

∴ C.P of the radio set for Sally = S.P of the radio set for Sally = 375 \$

since Sally sold the radio set to Thomas at a loss of 10 %.

∴ Loss = 10% of 375 \$ = [10/100] × 375 = 37.50 \$

Selling price of the radio set for Sally = C.P - Loss

= 375 \$ - 37.50 \$ = 337.50 \$

∴ C.P of the radio set for Thomas = 337.50 \$.

Hence Thomas bought the radio set for 337.50 \$.

3. A dealer bought 80 cricket bats for Rs.50 each. He sells 20 of them at a gain of 5% . At what gain % must he sell the remainder so as to gain 10 % on the whole ?

Solution:

We have ,

C.P of one bat = Rs.50.

∴ C.P of 20 bats = Rs ( 50 × 20 ) = Rs. 1000

Gain on these bats = 5 %

∴ S.P of 20 bats = Rs.[ [100 + Gain%] ∕ 100 ] × C.P

= Rs.[ [ 100 + 5 ] ∕100 ] × 1000 = Rs.1050

Now , C.P of 80 bats = Rs.( 80 × 50 ) = Rs. 4000, Desired gain = 10 %

S.P. required = Rs.[ [100 + Gain%] ∕ 100 ] × C.P

= Rs.[ [ 100 + 10 ] ∕100 ] × 4000 = Rs. 4400

Thus , desired S.P. of 60 bats = Rs. 4400 - Rs. 1050 = Rs. 3350

C.P. of 60 bats = Rs. ( 60 × 50 ) = Rs. 3000.

Desired gain on 60 bats = Rs. 3350 - Rs. 3000 = Rs. 350

Hence , desired gain % = [ [ 350 /3000 ] × 100 ] % = 11 ⅔ %