Profit and Loss Problems with Solutions for Bank Exams

Profit and loss problems asked frequently in the competitive exams. But many students are puzzled how to solve profit and loss problems, and mostly 12th passed students face difficulty. So those students who are preparing for SSC or bank exams can practice profit and loss problems with solutions.

Here you can learn easily how to solve the profit and loss problems with solutions and after that you can practice important question of profit and loss for SSC.  

Profit and Loss Problems with Solutions for Competitive Exams

Q.1. A man buys an article for Rs. 27.50 and sells it for Rs. 28.60. Find his gain percent.

Solution:

C.P = Rs. 27.50, S.P. = Rs. 28.60

So, Gain = Rs. (28.60 – 27.50) = Rs. 1.10.

 $$ ∴ Gain\% =  \left({1.10\over27.50}× 100\right)\%= 4\% $$

Q.2. If a radio is purchased for Rs. 490 and sold for Rs. 466.50, Find the loss percent.

Solution:

C.P. = Rs. 490, S.P = Rs. 465.50

Loss = Rs. (490 – 465.50) = Rs. 24.50

$$ ∴ Loss\% =  \left({24.5\over490}× 100\right)\%= 5\% $$ 

Q.3. Find S.P, when 

(i) C.P = Rs. 56.25, Gain = 20%

(ii) C.P. = Rs. 80.40, Loss = 5%

Solution:. (i) S.P = 120% of Rs. 56.25  $$ = Rs   \left({120\over100}× 56.25\right)= Rs\ 67.50 $$

Solution: (ii) S.P = 85% of Rs. 80.40  $$ = Rs   \left({85\over100}× 80.40\right)= Rs\ 68.34. $$

Q.4. Find C.P., when 

(i) S.P. = Rs. 40.60, Gain = 16%

(ii) S.P = Rs. 51.70, Loss = 12%

Solution:(i) C.P $$ = Rs   \left({100\over116}× 40.60\right)= Rs\ 35. $$

Solution: (ii) C.P$$ = Rs   \left({100\over88}× 51.70\right)= Rs\ 58.75 $$

Q.5. A person incurs 5% loss by selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit ?

Solution: 

 Let the new S.P be Rs. X. Then,

(100 – loss%) : (1st S.P.) = (100 + gain%) : ( 2nd SP.)

$$ →   \left({100-5\over1140}\right)=\left({100+5\over x}\right)→ \ x = \left({105+1140\over 95}\right)=1260. $$

Q.6. If the cost price is 96% of the selling price, then what is the profit percent?

Solution:  

Let S.P = Rs. 100. Then, CP = Rs. 96; Profit = Rs.4.

 $$ ∴ \ Profit \% =    \left({4\over96}× 100\right)\% = {25\over6}\% = 4.17% $$

Q.7. The C.P of 21 articles is equal to S.P of 18 articles. Find the gain or loss percent.

Solution: 

Let C.P of each article be Re. 1

Then, C.P of 18 articles = Rs.18, S.P of 18 articles = Rs. 21.

$$ ∴ \ Gain \ =    \left({3\over18}× 100\right)\% = 16{2\over6}\%  $$

Q. 8. A man bought toffees at 3 for a rupee. How many for a rupee must he sell to gain 50%?

Solution:  

C.P of 3  toffees = Re. 1; S.P of 3 toffees = 150% of $$ Re. 1= {3\over2} $$

For Rs. 3/2, toffees sold = 3 for Re. 1, $$ toffees \ sold  =  \left( 3×{3\over2}\right) = 2. $$

Q.9. 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% ?

Solution: . 

C.P of 200 kg of mixture = Rs. (80 x 13.50 + 120 x 16) = Rs. 3000

S.P. = 116% of Rs. 3000 ∴ \ = Rs.    \left({116\over100}× 3000\right) = Rs.3480  $$

∴ Rate of S.P of the mixture $$ ∴ \ = Rs.    \left({3480\over200}\right) = per \ kg \ = Rs.17.40 \ per \ kg.  $$

Q.10. A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. What was the cost price of the article ?

Solution:  

Let C.P. be Rs. X Then, (105% of x) – (80% of x) = 100 or 25% of x = 100

 ∴ x/4 = 100 or x = 400

So C.P = Rs. 400.

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