## Aptitude :: Profit And LossPage 1

Cost Price = C.P.
Selling Price = S.P.

If S.P. is greater than C.P., the seller is said to have a profit or gain.

If S.P. is less than C.P., the seller is said to have incurred a loss.

If an article is sold at a gain of say 25%, then S.P. = 125% of C.P.

If an article is sold at a loss of say, 25% then S.P. = 75% of C.P.

Loss or gain is always reckoned on C.P.

1. Gain = S.P. - C.P.

2. Loss = C.P. - S.P.

3. Gain Percentage:
Gain % =Gain x 100/C.P.

4. Loss Percentage:
Loss % = Loss x 100/C.P.

5. Selling Price: (S.P.)
S.P. = (100 + Gain %)/100 X C.P

6. Selling Price: (S.P.)
S.P. = (100 - Loss %)/100 X C.P.

7. Cost Price: (C.P.)
C.P. = 100/(100 + Gain %) X S.P.

8. Cost Price: (C.P.)
C.P. = 100/(100 - Loss %) X S.P.

9. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:
Loss % = (Common Loss and Gain %/10)2 = (x/10)2

10. If a trader professes to sell his goods at cost price, but uses false weights, then
Gain % = [Error/(True Value) - (Error) X 100]%

1.

 A man buys an article for Rs 27.50 and sells it for Rs 28.60. Find his gain percent ? (a)4% (b)5% (c)6% (d)7%
Answer is: ACP = Rs 27.50,
SP = Rs 28.60
So, Gain = Rs (28.60 - 27.50) = Rs 1.10
∴ Gain% = (1.1027.50 x100)% = 4%

2.

 A person incurs 5% loss by selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit? (a)1160 (b)1200 (c)1260 (d)1300
Answer is: CLet the new SP be Rs x Then,
(100 - loss%) : (1st SP) = (100 + gain%) : (2nd SP)
[(100 - 5)/1140] = [(100 - 5)/x]
? x = (105 x 1140/95) = 1260
? New SP = Rs 1260

3.

 A book was sold for Rs. 27.50 with a profit of 10%. If it were sold for 25.75, then what would have been the percentage of profit or loss? (a)1% (b)2% (c)3% (d)4%
Answer is: CSP = Rs. 27.50, Profit = 10%.
So, CP = Rs. (100/110 x 27.50) = 25
When SP = Rs 25.75, Profit = (25.75 - 25) = 0.75
∴ Profit % = (0.75/25 x 100)% = 3%

4.

 The CP of 21 articles is equal to SP of 18 articles. Find the gain or loss percent. (a)16 + (2/3)% (b)17% (c)17 + (2/3)% (d)18%
Answer is: ALet CP of each article be Rs 1
Then, CP of 18 article = Rs 18,
SP of 18 articles = Rs 21
∴ Gain % = (3/18 x 100)% = 16 + (2/3)%

5.

 By selling of 33 metres of cloth, one gains the selling price of 11 metres. Find the gain percent. (a)30% (b)40% (c)50% (d)60%
Answer is: CThen, (SP of 33 m) - (CP of 33 m)
Gain = SP of 11 m
∴ Let CP of each metre be Re 1
Then CP of 22 m = Rs 22,
SP of 22 m = Rs 33
∴ Gain % = (11/22 x 100)% = 50%

6.

 A vendor bought bananas at 6 for Rs 10 and sold them at 4 for Rs 6. Find his gain or loss percent. (a)10% (b)20% (c)25% (d)30%
Answer is: ASuppose, Number of bananas bought = LCM of 6 and 4 = 12
⇒CP = Rs (10/2 x 12) = Rs 20
SP = Rs (6/4 x 12) = Rs 18
⇒ Loss % = (2/20 x 100) = 10%

7.

 A grocer purchased 80 kg of sugar at Rs 13.50 per kg and mixed it with 120 kg sugar at Rs. 16 per kg. At what rate should he sell the mixture to gain 16%? (a)15 per kg (b)16 per kg (c)17 per kg (d)17.40 per kg
Answer is: DCP of 200 kg of mixture = Rs (80 x 13.80 + 120 x 16)
= Rs. 3000
SP = 116% of Rs 3000
= Rs (116/100 x 3000) = Rs 3480
∴ Rate of SP of the mixture = Rs (3480/200) per kg
= Rs 17.40 per kg

8.

 A man bought toffees at 3 for a rupee. How many for a rupee must he sell to gain 50%. (a)2 (b)3 (c)4 (d)5
Answer is: ACP of 3 toffees = Rs 1
SP of 3 toffees = 150% of Rs 1 = 3/2
For Rs 3/2, toffees sold = 3 For Rs 1
toffees sold = (3 x 2/3) = 2