Students and Teachers Forum

1. When will a sum of Rs. 400 amounts to Rs. 625 at the rate of 25% p.a. compound interest payable yearly?

Given,         Principal (P) = Rs. 400         Compound Amount (CA) = Rs. 625         Rate (R) = 25%         Time period (T) = ? We know, Compound Amount (CA) = P (1 + .....

2. Jamuna lends a sum of money to Kamana at the rate of 8% p.a. compound interest. If at the end of 2 years, Kamana clears the debt by paying Rs. 8748 to Jamuna, what sum of money does Jamuna lends to Kamana?

Given,         Rate (R) = 8%         Time (T) = 2 years         Amount (A) = Rs. 8748.         Principal (P) = ?   We know,         Amount (A) = .....

3. A sum of Rs. 900 is borrowed. If the rate of compound interest is 10% p.a. what amount paid at the end of the 2 years will clear the debt?

Given,          Principal (P) = Rs. 900          Rate (R) = 10% p.a.          Time (T) = 2 years          Compound amount (CA) = ?  We .....

4. Shyam deposited Rs. 5000 at 8% p.a. compound interest on the bank. Find the difference between the amount compounded yearly and half yearly.

Given, Principal (P) = Rs. 5000 Rate (R) = 8% p.a. We know, For yearly rate of interest, Amount (A1)     = P (1 + R100 )T                            = 5000 (1 + .....

5. According to the system of yearly compound interests, a sum of money amounts to Rs.12100 and Rs.13310 in 2 years and 3 years respectively. Find the sum and rate of interest.

Let the sum of money be Rs.x. According to question, When, Time (T1) = 2 years Amount (A1) = Rs.12100 When, Time (T2) = 3 years Amount (A2) = Rs.13310 Principal (P) = ? Rate of interest (R) = ? We know, Amount (A1) = P (1 + R100)T1     .....

6. Ram borrowed Rs. 4800 from Sita at the rate of 10% p.a. At the end of one year,
(i) how much compound interest will Ram have to pay?
(ii) how much compound interest semi-annually will Ram have to pay?

Given,       Principal (P) = Rs. 4800       Rate of interest (R) = 10% p.a       Time (T) = 1 year       Compound interest = ?       Compound interest compounded .....

7. Niru borrows sum of money from a company at the rate of 5% per annum compound interest. If at the end of 2 years she pays Rs. 246 as a compound interest, what sum does she borrow?

Given,          Rate (R) = 5%          Time (T) = 2 years          Compound interest (CI) = Rs.246.          Principal (P) = ? We know,   .....

8. A sum of money increased by its 0.05 in every 6 months after how long time the annual compound interest on Rs. 4000 will be Rs. 1324?

Here,        Rate of increase of money semi-annually ( 6-months) (R) = 0.05 = 5 / 100 = 5%        Hence, the rate of increase of money annually (R) = 5% × 2 = 10%        The .....

9. The marked price of an article is Rs. 4000. After allowing some discount and levying 13% VAT, the price of the article becomes Rs. 3616. Find the discount percent and the discount amount.

Given,         Marked price (MP) = Rs. 4,000         VAT = 13%         S.P. with VAT = Rs. 3616  Let x be the selling price without VAT.  Then,       .....

10. The price of an article including 15% VAT is Rs. 1380, find the price of the article before adding VAT.

Given, S.P. with VAT = Rs. 1380  Rate of VAT = 15%  S.P. before VAT =? S.P. before VAT = x (suppose)  Now,  S.P. with VAT = S.P. + VAT% of S.P. Or, 1380 = x + 15% X x Or, 1380 = x + 15/100 × x  Or 1380 = x + .....

11. Marked price of an article is Rs. 1500. What is the selling price with 10% VAT?

Given, Marked price of article (MP) = Rs.1500 VAT = 10% SP with VAT =? We know, Selling price with VAT      = Marked price + VAT amount                           .....

12. If $ 5 = £ 4 and Rs. 315 = $ 3, how many pound £ will be equal to Rs. 13125?

Here, $ 5 = £ 4 £ x (say) = Rs. 13125 Rs. 315 = $ 3 Using chain rule,         5  × x  × 315 = 4  × 13125 × 3   Or, 1575x = 157500 Or, x = 1575001575 Or, x = .....

13. Using the rate or Rs. 154 per Euro, calculate the Euro for Rs. 2800.

Here,       Rs. 154 = 1 Euro Or,  Re. 1 = 1154  Euro Or, Rs. 2800 = 1154 × 2800 Euros Or, Rs. 2800 = 18.18 Euros So, 18.18 Euros is equivalent to Rs. .....

14. After allowing 20% discount on the marked price and then levying 10% VAT, the radio was sold. If buyer had paid Rs. 320 for VAT, how much had he got the discount?

Let ‘x’ be the marked price. Now, Selling price (SP) = MP - discount % of MP Or, SP = x – 20% of x            = x - 20100 ⨯ x            = x - x5   .....

15. If 90 dollars = 75 Euro, 60 Euro = 89.10 Swiss Francs, 56 Swiss francs = £ 25 and £ 1 = Rs. 134.40, how many rupees are equivalent to 500 dollars?

Given,             $ 90 = 75 Euro              60 Euro = 89.10 Swiss Francs               56 Swiss francs = £ 25      .....

16. The price of an article with 15% VAT is Rs. 690. What will be the price excluding VAT?

Given,  Price with VAT = Rs.690 VAT % = 15% Let, the price excluding VAT = Rs. x Then, Price with VAT = x + 15% of x Or, Rs. 690 = x + 15100 ⨯ x Or, Rs. 690 = x + 3x20 Or, Rs. 690 = 23x20 Or, x = Rs. 2023 ⨯690  Or, x .....

17. Find the sales tax on the purchase of goods worth Rs. 62,500 at 12%.

Here, Price of goods = Rs.62500 Tax = 12%. Now, Sales tax =12% of Rs. 62500                = 12100  × Rs.62500                = Rs. 7500  So, the .....

18. Allowing 20% discount on the marked price of a watch, the value will become Rs. 2376 when a VAT of 10% is added. Find the marked price.

Let the marked price be Rs ‘x’. Then, SP = MP - D% of MP      = x – 20% of x       = x - 20100 ⨯ x      = x - x5      = 4x 5 Now,  SP with VAT =  .....

19. If the exchange rate between Nepal and Japan is Rs.100 for 2000 yens, between Nepal and the USA Rs 100 for $ 1, between the USA and France, 1 dollar for 2.5 francs, what is the arbitrary rate of exchange between France and Japan?

Here,     Let, 1 francs = x yens          2000 yens = Rs. 100              Rs. 100 = 1$                      1$ = 2.5 .....

20. Find the arbitrary rate of exchange between Newyork and Kathmandu from the following data:
Rs. 135.75 = £1,     £2 = 3 Euro,     $9 = 11.25 and 18.1 Swiss francs = 12 Euro. 
 

Given,                 Rs. 135.75 = £ 1                             £ 2 = 3 Euro          .....

21. A person buys an article at a discount of 13% and pays 16% VAT. If he pays Rs. 261 for VAT, find the marked price of the article and also the amount paid by him to buy the article.

Given,          VAT amount = Rs. 261           Rate of VAT = 16%           Rate of discount = 13%  S.P. before VAT = x (suppose)   Now, we have .....

22. The marked price of an article is Rs. 2200. After allowing a certain percent of discount, 13% VAT is charged and the article is sold for Rs. 2063.38. Find the discount percent.

Given,         Marked price (M.P.) = Rs. 2200         Rate of VAT = 13%         S.P. with VAT = Rs. 2063.38         Discount % =? Let S.P. without .....

23. After allowing 25% discount on the marked price and then levying 10% VAT, a cycle was sold. If the discount amount was Rs. 750, how much VAT was levied on the price of the cycle?

Given,     Discount = 25%      VAT = 10%      Discount amount = Rs 750      VAT amount =? Let the Marked price (M.P.) be Rs. x. We know, Discount amount = D% of M.P.  Or, Rs. 750 = 15100 .....

24. After allowing 25% discount on the marked price of a cycle, 15% VAT was levied on it. If the cycle was sold for Rs. 3450, what was the marked price of the cycle?

Given,     S.P. with VAT = Rs. 3450      Discount percent = 25%      VAT = 15%      Marked price (M.P.) = x (suppose)  We know, S.P. = M.P. - D% of M.P.        = x - .....

25. Prakash bought 100 Nepali caps at Rs. 250 each, if he sells all the caps at 10% profit. How much money he gets at Toronto?
[1 canadian dollar = Rs.95]

Given,     Cost of each cap = Rs. 250      Number of caps = 100  ∴ Total cost (C.P.) = 100 × Rs. 250                              .....

26. The present buying rate of 1 Euro is Rs. 110. If Nepali money is revaluated by 20% then how much Euro can be exchanged at Rs. 200000?

Here, Before revaluation, €1 = Rs. 110 After 20% revaluation in Nepali money, €1 = Rs. 110 - 20% of Rs. 110      = Rs. 110 - 20100 ⨯ Rs. 110      = Rs. 110 -  Rs. 22      = .....

27. A tourist buys a statue for Rs. 5085, after allowing a discount of 10% and adding 13% VAT. How much does he get back while leaving Nepal?

Given, S.P. with VAT = Rs. 5085  Discount = 10%  VAT = 13%  Marked price M.P. = x (suppose)  We know, S.P. without VAT = M.P. - D% of M.P.                          .....

28. A merchant in Nepal buys goods in London to the value of £ 1000. Find the value of the goods in N.C; when the rate of exchange between India and Nepal is Rs. 1.60 (N.C.) for Re. 1 (I.C.) and between London and India is £ 100 = Rs. 8425 (I.C.)

Let the value of goods in N.C. be Rs. x  Now,  (N.C.) Rs. x = £ 1000             £ 100 = Rs. 8425 (I.C.)    Re. 1 (I.C.) = Rs. 1.60 (N.C.) , Using chain rule, we get    .....

29. Reshma bought 5000 flags at the rate of Rs. 125 in Nepal and exported to US and makes a profit of 175%. Find the selling price of flags in $. [$ 1 = Rs. 81]

Given, Cost of one flag = Rs. 125 Cost of 5000 flags = 5000 × Rs.125                                         = Rs. .....

30. The price of an article with 13% VAT is Rs. 1356. Find the price of the article excluding VAT. 

Given, S.P. with VAT = Rs. 1356  Rate of VAT = 13%  Price excluding VAT (S.P.) =? Let the price excluding VAT (S.P.) = x   Then, S.P. with VAT = S.P. + VAT% of S.P.  Or, Rs. 1356 = x + 13% of x  Or, Rs. 1356 = x .....

31. If Rs. 1000 = $ 125, $ 25 = 30 Euro, 10 Euro = 15 Singapore dollars. Express 450 Singapore dollars in Rupees.

Given,             Rs. 10000 = $ 125                      $ 25 = 30 Euro               10 Euro = 15 Singapore .....

32. Pound sterling 1 can be bought at Rs. 130. 2% commission should be paid to exchange Rs. 250000 into pound sterling. What amount of pound sterling can be received? Find it.

Given,          £1=Rs. 130          Commission = 2 %. Now, Amount to be exchanged after commission = Rs. 250000 - 2% of Rs. 250000                  .....

33. At present 1 Euro can be bought at Rs. 110. If Nepali money is devaluated by 10% then what is the cost of 50 Euro?

Here, Before devaluation, €1 = Rs. 110 Now, after 10% devaluation in Nepali money, €1 = Rs. 110 + 10% of Rs. 110       = Rs. 110 + 10100 ⨯ Rs. 110      = Rs. 110 + Rs. 11      = Rs. .....

34. The present buying rate of 1 US dollar is Rs. 105. If Nepali money is devaluated by 20% then how much US dollar can be exchanged at Rs. 200000?

Here, Before devaluation, $1 = Rs. 105 Now, after 20% devaluation in Nepali money, $1 = Rs. 105 + 20% of Rs. 105      = Rs. 105 + 20100 ⨯ Rs. 105      = Rs. 105 + Rs. 21      = .....

35. The price of an article with 13% VAT is Rs. 2034. What is the price of the same article without VAT?

Let, x be the price of an article without VAT. Then,          Price of an article with VAT = Rs. x + 13% of Rs. x  Or,   2034 = x + 13100  × x Or,   2034 = 113x100 Or,  .....

36. A radio costs Rs. 3200 without VAT and Rs. 3600 including VAT. Find the VAT amount and the VAT percent.

Here, Cost of radio without VAT = Rs. 3200 Cost of radio with VAT = Rs. 3600 So,   VAT amount = CP with VAT – CP without VAT                       = Rs. 3600 – Rs. .....

37. Find the total selling price of a shirt whose marked price is Rs. 2700 when 13 % VAT is levied?

Here, Marked price of the shirt (MP) = Rs.2700 VAT% = 13% Now, The selling price of a shirt is given by,  SP = MP + VAT% of MP      = Rs. 2700 + 13% × Rs. 2700      = Rs. 2700 + 13100 × Rs. .....

38. Rs.60,000 is exchanged with US $. Next day the Nepali currency is devaluated by 10%, how much Nepali currency is needed to exchange the same amount of US $? Also find the loss made in this one day.

Let the initial rate be Rs. 100 for $ 1. Since, the Nepali currency is devaluated by 10%, The rate after devaluation is Rs. 110 for $ 1.  Now,  Rate             Cost  100    .....

39. The marked price of an article is Rs. 4500. After allowing some percent of discount with 10% VAT levied on it, the article is sold at Rs. 4400. Find the discount percentage.

Here, MP =  Rs.4500 Final price with VAT = Rs.4400 We know, Price with VAT = SP +VAT % of SP Or, 4400 = SP + 10100  × SP Or, 4400 = 1110 SP Or, SP = Rs.4000 Again,  Discount amount = MP - SP         .....

40. After allowing 20% discount and levying 13% VAT, a customer had paid Rs. 520 for VAT. How much had he got the discount? Find it.
 

Here,      Discount percent (D %) = 20%      VAT percent (VAT %) = 13%      Vat amount = Rs. 520 We have,        VAT amount = VAT percent of SP Or, Rs. 520 = 13% × SP Or, 520 = .....

41. A dealer sold a photocopy machine for Rs. 420000 plus 13% VAT to the retailer. If the retailer spent Rs. 2500 on transportation cost, Rs. 4000 on local tax and made Rs. 20000 profit and then supplied to the photocopy centre, how much did the photocopy centre pay the VAT amount at the present rate of VAT?

Here, Total cost paid by the retailer (CP)= (Cost of a photocopy + VAT percent of Cost of photocopy) + Transportation cost + Local .....

42. $1 can be bought at Rs. 105. To visit foreign country Abdul has to exchange $ 3500. If the bank charges 2% commission then what amount of Nepali rupees is required?

Given,     $1 = Rs. 105     Commission = 2%. Now, Amount to be exchanged after commission = $3500 - 2% of $ 3500                                .....

43. An electric fan, after allowing a discount of 15% on its marked price, was sold at a gain of 20%. Had it been sold after allowing 25% discount there would have been a gain  of Rs. 120. Find the cost price of the fan.

Let , the MP of the electric fan = Rs. x In case I, Discount % = 15% We know,       SP = MP - Discount% of MP or,  SP = MP – 15% of MP            =  x - 15100 × x     .....

44. 10 tolas gold bought from American market at $553 per tola is sold in Nepal at 20% customs duty charge and 13% VAT. At what price should it be sold?

Here,       1 tola = $ 553 Or, 10 tola = 10 x $ 553                   = $ 5530  Total amount after 20% customs duty charge = $5530 + 20% of $ 5530       .....

45. Find the net selling price of a shirt marked at Rs. 1200 when the VAT of 13% is levied.

Here, Marked price of the shirt (MP) = Rs.1200 VAT = 13%. Then, The selling price of the shirt is given by,  SP = MP + VAT% of MP       = Rs. 1200 + 13% × Rs. 1200       = Rs. 1200 + 13100 .....

46. 500 Bhadgaule Topi brought for Rs. 400 per piece in Nepali market was sold in Britain after levying 5% tax. During the transaction, 150% profit was made. Find the selling price of each Topi.

Here, Cost price of of Topi (CP) = Rs. 400 Tax rate  = 5% Now, Price after tax levied = Rs. 400 + 5% of Rs. 400                                   = Rs. 400 + .....

47. Of the total candidates in an examination, 40% students passed in Mathematics, 45% in Science and 55% in Health. If 10% passed in math and science, 20% in science and health, and 15% in health and maths:
i) Draw the information in Venn diagram.
ii) Calculate the number of students passing in all three subjects.

Let A, B and C be the set of students passing in mathematics, science and health respectively. Then, Percentage of students passing in mathematics, n(M) = 40% Percentage of students passing in science, n(S) = 45% Percentage of students passing in .....

48. Each student in a class of 40 plays at least one indoor game chess, carrom and scrabble. 18 play chess, 20 play scrabble and 27 play carrom. 7 play chess and scrabble, 12 play scrabble and carrom and 4 play chess, carrom and scrabble.
Find the number of students who play
(i)  chess and carrom.
(ii) chess, carrom but not scrabble. 

Let A be the set of students who play chess, B be the set of students who play scrabble and C be the set of students who play carrom.  Then, Number of students who play chess, n(A) = 18 Number of students who play scrabble, n(B) = 20   .....

49. Out of 1350 candidates, 600 passed in Science, 700 in Maths, 350 in English and 50 failed in all the three subjects. If 200 passed in Science and Maths, 150 in science and English, 100 in Maths and English,how many candidates passed in all three subjects?

Let S, M and E denote the sets of students passed in Science, Maths and English respectively. Then from question, Total number of candidates, n(U) = 1350 No. of candidates who passed in Science, n(S) = 600 No. of candidates who passed in Maths, n(M) .....

50. In a cold store shop, out of 100 customers questioned, 50 like coke, 30 like pepsi, 40 like frooti, 20 like coke and pepsi, 18 liked coke and frooti, 12 like pepsi and frooti, 5 liked all of the three drinks. Find how many liked 
(a) at least one of the three drinks 
(b) exactly two types of drink 
(c) exactly one type of drink 
(d) none of the drinks 
(e) Represent all information in a venn-diagram.

 

Let, Total number of customers questioned, n(U) = 100 No. of customers who like coke, n(C) = 50 No. of customers who like pepsi, n(P) = 30 No. of customers who like frooti, n(F) = 40 No. of customers who like coke and pepsi, n(C∩P) = 20 No. of .....