1. The average weight of 31 students was calculated as 26kg. It was later found out that there was error in calculating the weight. One boy whose weight was 25kg was calculated as 21kg and one boy whose weight was 26kg was calculated as 29kg. Find the difference between correct average and erroneous average (in kg).
2. The ratio of the base radius and the height of a right circular cone is 3:4. The curved surface area of the cone is 2310 sq cm. What is the volume of the cone?
Ans:2 Let the base radius and the height of the cone be 3x and 4x respectively.
Slant height of the cone = √(9x2 + 16x2) = 5x
Curved surface area of the cone = π (3x) (5x) = 2310
x2 = 49
x = √49 = 7 cm
Therefore the volume of the cone = (1/3)π[(3*7)2 (4*7)]
= 12936 cu cm.
3. A and B entered into a partnership. A invested Rs 5000 and B invested an amount equal to Rs 2000. After 3 months A withdrew Rs 1000 and B invested Rs 1000 more. What must be the profit at the end of the year if A receives a share of Rs 17,000?
Ans:4 All money units are in Rs. ∵ A withdrew 1000 after 3 months, he had 5000 invested for 3 months and 4000 invested for remaining 9 months. ∵ B invested 1000 more after 3 months, he had invested 2000 for 3 months and 3000 for remaining 9 months. A’s total investment = capital X Time = 5000 X 3 + 4000 X 9 = 51000 B’s total investment = 2000 X 3 + 3000 X 9 = 33000 Ratio of investments = 51000:33000 = 51:33 = 17:11 Sum of parts of ratio = 17 + 11 = 28 Let the profit at the end of the year be ‘p’ A’s share = (17/28) X p=17000 => p=(28 X 17000)/17 => p = 28,000
4. Dinesh’s monthly income is 25% more than monthly income of Eswar. While, Eswar saves 20% more than Dinesh. Dinesh’s monthly income is Rs.12000/- and his monthly savings are Rs. 3000/-. What is the annual expenditure of Eswar?
Ans:4 Given that, monthly income of Dinesh = Rs.12000/- Therefore monthly income of Eswar = (Rs.12000) ÷ [1 + 25/100] = Rs.9600/-. Monthly savings of Dinesh = Rs.3000/- Therefore monthly savings of Eswar = [1 + 20/100] 3000 = Rs.3600/- Therefore annual expenditure of Eswar = 12 * Rs. (9600 – 3600) = Rs.72000/- Hence the correct option is D.
5. A manufacturer marked his article up by 38% on the manufactured price and sold it at a profit of 15%. Had he sold it for Rs.600 more he would have gained 30% profit. Find the difference between marked price of the article and selling price of the article when sold at 24% profit.
Ans:3 Let manufacturing cost = Rs.100P Marked price = 138% of 100P = Rs.138P SP when sold at 15% profit = 115% of 100P = Rs.115P SP when sold at 30% profit = 130% of 100P = Rs.130P According to question- => 130P – 115P = 600 => P = 40 Marked price of article = 138P = 138 * 40 = Rs.5520 SP when sold at 24% profit = 124% of 100P = 124P = 124 * 40 = Rs.4960 Required difference = 5520 – 4960 = Rs.560
6. Three cards are drawn randomly from a pack of 52 cards. What is the probability that one will be black and two will be red?
Ans:3 3 cards can be drawn from a pack of 52 cards in 52C3 ways.
1 black card can be drawn in 26C1 ways and 2 red cards can be drawn in 26C2 ways.
7. The cost price of a car is 400% more than that of a bike. If the cost of a car increases by 14% and that of a bike by 12%, then the total percentage increase in the cost price of 5 cars and 15 bikes is :
Ans:1 Let the cost of a bike= Rs X Then cost of car=4X+X=5X Initial cost of 5 cars and 15 bikes is=5*5X+15X=25X+15X=40X Changed cost=25X*(114/100)+15X*(112/100)=28.5X+16.8X=45.3X Hence, percentage change=[(45.3X-40X)/ 40X]*100=(5.3/40)*100=13.25%
8. A borrows an amount of Rs.36000 from B at 20% simple rate of interest for 2 years and lent 75% of this amount to C at 20% compound rate of interest for 2 years. Remaining he used for his personal purpose. Find the total loss incurred by person A.
Ans:3 Total amount given by A to B at the end of 2 years = 36000 + [(36000 * 20 * 2)/100] = Rs.50400
Amount lent to C = 75% of 36000 = Rs.27000
Total amount received by A from C = 27000 * (1.2)2 = Rs.38880
Total loss incurred by A = 50400 – 38880 = Rs.11520
9. After travelling for 3 hour and 15 minutes at a speed of 40 km/hr Vishnu realized that he has covered only 5/8 of the total distance. If he has to cover the entire distance in 4.5 hours then at what speed he should travel for the remaining time period?
Ans:2 Total distance covered by Vishnu in 3 hour 15 minutes = (40 X 3.25) km = 130 km Now total distance that Vishnu has to cover = (130 X 8/5) km = 208 km Now remaining distance that Vishnu has to travel = (208 – 130) km = 78 Km Now the speed of Vishnu for the remaining period = (78/1.25) km/hr = 62.4 km/hr
10. Construction of a wall is to be completed in 45 days and 110 men are working 8 hours a day. After 25 days, 2/5th of the work is finished. How many extra men must be employed so that the work must be completed on time assuming each man is now working 10 hours?
Ans:2 Total work done in 25 days = 25 X 110 X 8 man – hours (MH) = 200 X 110 MH = 22000 MH Now remaining work = (22000 X (3/5)/(2/5)) MH = 33000 MH Total remaining days = 45 – 25 = 20 days Let’s suppose number of additional men required = N Hence, (110 + N) X 20 X 10 = 33000 => 110 + N = 165 => N = 55
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