1. QUESTIONS ON AVERAGE, PERCENTAGE & PROFIT by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india FOR – PGPSE / CSE PARTICIPANTS mobile : 91+9414430763

2. My words.... Here I present a few basic questions on average, percentage & profit . I wish that more people should become entrepreneurs. An ordinary Indian entrepreneur wishes to remain an honest entrepreneur and contribute to the development of nation but we have to strengthen those institutions which truly promote entrepreneurship, not just degree granting institutions. Let us work together to promote knowledge, wisdom, social development and education. We believe in free education for all, free support for all, entrepreneurship opportunities and training for all. Let us work together for these goals. ... I alone cant do much, I need support of perosns like you .......... ...

3. 1 liter of water is add to 5 liters of a 20 % solution of alcohol in water . Find the strength of alcohol in new solution? At present we have 1 liter alcohol and 4 liters water. But now water becomes 5 liters. The strength of alchoal is : 1/(1+5) *100 = 16.66% answer

4. If A earns 33 1/3 more than B .Then B earns less than A by what percent? If B earns 100, A earns 133.33 B earns 33.33 less than A or in % : 33.33 / 133.33 *100 = 25% answer

5. A school has only three classes which contain 40,50,60 students respectively.The pass percent of these classes are 10, 20 and 10 respectively . Then find the pass percent in the school. Number of students passing out : 4,10 and 6 from the 3 classes. Total pass = 20 total students = 150 pass percentage=20/150 *100 = 13.33%

6. There are 600 boys in a hostel . Each plays either hockey or football or both .If 75% play hockey and 45 % play football ,Find how many play both? Add 75+45 = 120, (120 -100 = 20), thus 20% play both the games. 120 students play both football and hockey. Answer

7. A bag contains 600 coins of 25p denomination and 1200 coins of 50p denomination. If 12% of 25p coins and 24 % of 50p coins are removed, Find the percentage of money removed from the bag ? Toal amount = (600 .25) + (1200* .5) = 750 amount of coins removed = (72*.25) + (288*.5) = 162 162/750 * 100 = 21.6% answer

8. P is six times as large as Q.Find the percent that Q is less than P? Let us assume Q = X P = 6X Q is less by (6X – X) = 5X 5X/6X * 100 = 83% approximately. Answer

9. For a sphere of radius 10 cm ,the numerical value of surface area is what percent of the numerical value of its volume? Volume of shpere = 4/3 * pi * r^3 surphace area of sphere = 4pi*r^2 ratio of surface area to volume = 4pir^2 / 4/3pir^3 * 100 = 3/10 * 100 = 30% answer

10. A reduction of 21 % in the price of wheat enables a person to buy 10 .5 kg more for Rs 100.What is the reduced price per kg. Let us assume reduced price = X 100 /1.27X - 100 / X = 10.5 (100 – 127) / 1.27X = 10.5 -27 / (10.5*1.27) =x X = 2.02 answer

11. The average temperature of the town in the first four days of a month was 58 degrees. The average for the second ,third,fourth and fifth days was 60 degree .If the temperature of the first and fifth days were in the ratio 7:8 then what is the temperature on the fifth day? 1 st day = 7X, 5 th day = 8x Total for first 4 days : 58*4 = 232 total for 2,3,4,5 day = 60*4 = 240 difference between 5 th and 1 st day = 8X-7X or 240 -232 X = 8 temperature on fifth day = 8*8 = 64 degrees answer

12. The average of 5 numbers is 7.When 3 new numbers are added the average of the eight numbers is 8.5. The average of the three new number is? Total of first 5 = (5*7) = 35 total of 8 (including 3 new digits) = (8*8.5) = 68 total of 3 new digits = (68 – 35 = 33 average of 3 new digits=33/3 = 11 answer

13. Of the three numbers the first is twice the second and the second is twice the third .The average of the reciprocal of the numbers is 7/72,the numbers are Assume 3 rd number = x, 2 nd number = 2x and 1 st number = 4x actually the total is : 7/72 * 3 = 7/24 if we take average of reciprocals :, then 1/x + 1/2x + 1/4x = 7/4x 7/4x = 7/24 x = 7/24 * 4/7 = 1/6 x = 6, other two numbers are 12 and 24 answer

14. 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of groups B? Total of 16 children = (16 * 76) = 1216 total of group A = ( 10 * 75)= 750 total of group B = 466 average of B = 466 / 6 = 77.6 answer

15. The mean temperature of Monday to Wednesday was 37 degrees and of Tuesday to Thursday was 34 degrees .If the temperature on Thursday was 4/5th that of Monday. The temperature on Thursday was Total from Monday to Wednesday = (3 * 37) = 111 total from tuesday to thursday = (3* 34) = 102 difference between Monday and Thursday : 5X – 4X = (111 -102) = 9 X = 9, temperature on tursday = (4*9) = 36 answer

16. A man whose bowling average is 12.4,takes 5 wickets for 26 runs and there by decrease his average by 0.4. The number of wickets,taken by him before his last match is: Let us assume number of wickets taken before start of this match = x and number of runs = Y Y/X = 12.4 or Y -12.4X = 0 (Y+26) / (X +5) = 12 or Y-12X=34 X = 85 (number of wickets) Y = 1054 answer

17. A team of 8 persons joins in a shooting competition. The best marksman scored 85 points.If he had scored 92 points ,the average score for the team would have been 84.The team scored was. Total of team = (8*84) – (92-85) =672 – 7 =665 answer

18. The average weight of 3 men A,B and C is 84 Kgs. Another man D joins the group and the average now becomes 80 Kgs.If another man E whose weight is 3 Kgs more than that of D ,replaces A then the average weight B,C,D and E becomes 79 Kgs. The weight of A is. Weight of A+B+C = (3*84) = 252 Weight of A+B+C+D= ((4*80) = 320 weight of D = 320-252 = 68 weight of E= 71 total of B+C+D+E = (4*79) = 316 difference of A and E is just 4 Kg. (320-316) weight of A = 71+4 = 75 kg. Answer

19. Five years ago, the average age of P and Q was 15 years ,average age of P,Q, and R today is 20 years,how old will R be after 10 years? Total of P & Q = (15+5) * 2 = 40 total of P,Q,R = (20*3) = 60 R = 20 age of R after 10 years = 20+10 = 30 answer

20. The average age of the boys in the class is twice the number of girls in the class .If the ratio of boys and girls in the class of 36 be 5:1, what is the total of the age (in years) of the boys in the class? Number of girls = 1/(1+5) * 36 = 6 average age of boys = 2*6 = 12 Number of boys= 36-6 = 30 total age of boys=30*12 = 360 answer

21. .In a cricket eleven ,the average of eleven players is 28 years .Out of these ,the average ages of three groups of players each are 25 years,28 years, and 30 years respectively. If in these groups ,the captain and the youngest player are not included and the captain is eleven years older than the youngest players , what is the age of the captain? Total of 11 = (11*28) = 308 total of 3 groups (3*25 + 3*28 + 3*30) = (75+84+90) = 249 remaining = 59 Captain + Y = 59 C-Y= 11 2C = 70 or C = 35 answer

22. Dhoni scored 87 in his 17 th innings and this increased his average by 3. What is the new average of Dhoni ? Let us assume that his average is X total runs = (number of innings * the average run rate) = 17 *x 17x – 87 = 16(x-3) 17x – 87 = 16x – 48 x = 39 answer

23. The average weight of 24 students is 35 kg. If the weight of teacher is also included, the average rises by 400 grams. What is the weight of the teacher ? Let us assume the weight of teacher = x total weight earlier : (number of students * average weight) =24*35 = 840 new total weight = (24+1) * (35+.400) = 885 (difference is due to inclusion of teacher) weight of teacher = 885 – 840 = 45 Kgs.

24. Average earning of 11 days is 50000. the average for first 6 days is 49000 and the average for last 6 days is 52000. what is the earning on 6 th day? Total for 11 = (11 * 50000) = 550000 total for first 6 = (6*49000) = 294000 total for last 6 = (6*52000) = 312000 let us add the last two : 294000+312000 = 606000 find the difference of this and total of 11 : 606000 – 550000=56000 (which is income of the 6 th day)

25. Find the average of all these numbers.142,147,153,165,157. Formula for average = total for all / number of digits First add them all : total = 764 there are 5 digits so divide it by 5 = 764/5 = 152.8 answer

26. Find the average of all these numbers: 4,10,16,22,28 Total = 80 there are 5 digits so divide by 5 average = 80 / 5 = 16 answer shortcut = difference of all the numbers is equal, so mid value (16) is the average – so there is no need for all this calculation)

27. Find the average of all these numbers: =4,10,16,22,28,34. Here also we have same difference between continuous digits, so take the middle digits : middle digits are : 16 and 22. find the mid point of these two digits : (16+22)/2 = 19 or 16 + 3 (half of 6, which is common difference). Answer

28. The average marks of a student in 4 Examinations is 40.If he got 80 marks in 5th Exam then what is his new average. His total for 4 examinations = 160 total after 5 examinations = 160+80 = 240 new average = 240/5 = 48 answer

29. The average marks of Surabhi Daga in 10 Examinations is 80%.If she got 90 marks in 5th Exam then what is her new average. her total for 10 examinations = 800 total after 11 examinations =800+90 new average = 890/11 = 80.9 answer

30. In a group the average income of 6 men is 500 and that of 5 women is 280, then what is average income of the group. Total for men = (6*500) = 3000 total for women = (5*280) = 1400 total for all= 4400 there are 11 persons (6 men + 5 women), so average = 4400/11 = 400 per person.

31. The average weight of a class of 30 students is 40 kgs if the teacher weight is included then average increases by 2 kgs then find the weight of the teacher? Total for students = 30 * 40 = 1200 total with teacher (30+1) * (40+2) = 1302 the difference is due to teacher : 1302– 1200 = 102 kgs. Answer

32. The average age of Mr and Mrs Sharma (Ilahabad Wale) 4 years ago is 28 years . If the present average age of Mr and Mrs Sharma and their son is 22 years. What is the age of their son? Age of Mrs and Mr. Sharma : (28+4) * 2 = 64 age with son : (3*22) = 66 age of son = 66 – 64 = 2 years. Answer

33. The average price of 10 books is increased by 17 Rupees when one of them whose value is Rs.400 is replaced by a new book. What is the price of new book? Old price = 400 addition = 10 * 17 = 170 new price = 570 answer

34. The average marks of girls in a class is 62.5. The average marks of 4 girls among them is 60.The average marks of remaining girls is 63,then what is the number of girls in the class? Let us assume the number of students = X total = 62.5x (4*60)+(63 * ( X -4) = 62.5X 240+ 63X- 252 = 62.5x .5X = 12 X = 24 answer

35. Find the average of first 50 natural numbers? Just add 1 and divide by 2, you will get the mid point. Simply find the mid point (50+1) / 2 = 51/2 = 25.5 answer

36. The average of the first nine prime number is? Add them : (2+3+5+7+11+13+17+19+23) =100 now divide this total by 9, we get : 11.11 answer

37. The average of 2,7,6 and x is 5 and the average of and the average of 18,1,6,x and y is 10 .what is the value of y? Total of first 4 digits = (4*5 ) = 20 X = 20 – (2+7+6) = 5 total next 5 digits = (5*10) = 50 value of Y = 50 - (18+1+6+5) = 20 Y = 20 answer

38. The average of a non-zero number and its square is 5 times the number.The number is? Let us assume the number to be X X + X^2 = 2(5X) X^2 = 10x- X X^2 = 9X X = 9 answer

39. P and Q started a business investing Rs 85,000 and Rs 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively? Profit can be divided either in capital ratio or equally. Here we assume that profit is divided in capital ratio : 85:15 or 17:3 answer

40. P and Q started a business investing Rs 85,000 each. However, P withdrew 20% of his capital after 1.5 year and Q doubled his investment after 20 months. . In what ratio the profit earned after 2 years be divided between P and Q respectively? Profit can be divided either in capital ratio or equally. Here we assume that profit for 2 nd year is divided in capital ratio : p = (85*6 + 68*6) =918 Q = (85*6 + 170*6) =1530 their ratio : 918:1530 or 3:5 answer

41. A,B and C started a business by investing Rs 1,20,000, Rs 1,35,000 and Rs 1,50,000.Find the share of each ,out of an annual profit of Rs 56,700? Their profit sharing ratio as per their capital : 120: 135:150 or 8:9:10 share of A =8/27 *56700 = 16800 share of B = 9/27 *56700 = 18900 share of C = 10/27 *56700 = 21000 answer

42. A,B and C started a business by investing Rs 2,20,000, Rs 350000 and Rs 4,50,000.Find the share of each ,out of an annual profit of Rs 10200 ? Their profit sharing ratio as per their capital : 22:35:45 share of A =22/102 *10200 = 2200 share of B = 35/102 *10200 = 3500 share of C =45/102 *10200 = 4500 answer

43. 3 milkman A,B,C rented a pasture A grazed his 45 cows for 12 days B grazed his 36 cows for 15 days and c 60 cows for 10 days. If b's share of rent was Rs 540 What is the total rent? Share of A = 45*12 = 540 share of B = 36*15 = 540 share of C = 60 * 10 = 600 share of B's rent is 540, that means total rent is : (540+540+600) = 1680 answer

44. 3 milkman A,B,C rented a pasture A grazed his 90 cows for 6 days B grazed his 15 cows for 20 days and c 30 cows for 5 days. If C's share of rent was Rs 300 What is A's rent ? Share of A = 90*6 = 540 share of B = 15*20= 300 share of C = 30*5= 150 share of c's rent is 300, that meansthe rent is twice the total cow-days. So A's rent should be 1080 answer

45. Ram and Krishn entered into a partnership with Rs 50,000 and Rs 60,000, after 4 months Ram invested Rs 25,000 more while Krishn withdraw Rs 20,000 . Find the share of Ram in the annual profit of Rs 289,000. Ram's share = (50*4 + 75*8) =800 Krishn's share = (60*4 + 40*8) =560 share of ram = (80)/(80+56) * 289000 =170000 answer

46. A,B,C enter into partnership .A invests 3 times as much as B invests and B invests two third of what C invests. At the end of the year ,the profit earned is Rs 6600. what is the share of B? Let us start from C. Suppose C invests Rs. 3. B will invest 2/3 of 3 = 2. Thus A would invest 6 total investment = 11 share of B = 2/11 * 6600 = 1200 answer

47. A,B,C enter into partnership . A invests two third of what B invests and B invests two third of what C invests. At the end of the year ,the share of A is 2000, what is the share of B and C? (start with the last - here C) Suppose C invests (3*3) = 9 B will invest = 9 * 2/3 = 6 A will invest = 6 * 2/3 = 4 thus if share of A is known, we can find share of B and C also. B = 6/4 * 2000 = 3000 C = 9/4 * 2000 = 4500 shortcut = simply multiply 2000 *3/2 for B and again by 3/2 for C. You will get the answer

48. A,B and C enter into a partnership by investing in the ratio of 3:2:4. After one year ,B invests another Rs 2,70,000 and C,at the end of 2 years, also invests Rs 2,70,000.At the end of 3 years,profit are shared in the ratio of 3:4:5.Find the initial investment of each? Share of A = 3x*3 = 9x share of B = 2x*3 + 270*2 = 6x+540 Share of C =4x*3+270*1 = 12x+270 based on new ratio : 9x/3 = (12x+270)/5 3x=2.4x+54 or .6x=54 or x= 54/.6 = 90 so initial investments were : A : 270, B 180 and C 360 (all in thousands). Answer

49. A,B and C enter into a partnership by investing in the ratio of 3:2:4. After one year ,B invests another Rs 300,000 and C,at the end of 2 years, also invests Rs 300,000.At the end of 3 years,profit are shared in the ratio of 2:2:3 .Find the initial investment of each? Share of A = 3x*3 = 9x share of B = 2x*3 + 300*2 = 6x+600 Share of C =4x*3+300*1 = 12x+300 based on new ratio : 9x / 2 = (12x+300)/3 4.5x = 4x+100 or .5x = 100 or x = 200 initial investment by A = 600, B = 400 and C =800 (all in '000) answer

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53. 2^(2x-1) = 1/(8^(x-3)), what is x? Options : 3,2,0,-2 put x = 2 and you get the answer

54. 3^(4x-2) = 729, what is x? Options : 1,1.5,2,2.5, try to put the value x=2, you get the answer

55. 32^1/3 = 2^x, what is x? Options : 5,3,3/5,5/3 answer :

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