A regular pyramid has a square base with side 10 cm and a vertical height of 20 cm. If the height increases by 10% of its original value and the volume is constant, the percentage change in the side of the square base with respect to its original value is approximately :
Answer: C Volume of pyramid = 1/3 * 100*20 New height of pyramid = 22 cm. Let the new side of square be x cm. New volume = 1/3 * x2 * 22 sq. cm 1/3 * x2 * 22 = 1/3 * 100*20 => x = 9.5 percentage change in the side of square have => (10-9.5)/10 * 100 = 5% less.
Q. No. 14:
In a city, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. If the total population of the city is 728400, what is its female population ?
Answer: C Total migrants population = 35/100 * 728400 = 254940. Local population = 65/100 * 728400 = 473460 Total rural migrants = 20/100 * 254940 = 50988 Total urban migrants = 80/100 * 254940 = 203952 Population of females= (48/100 *473460) + (30/100 *50988) +(40/100 * 203952) => 227260.8 + 15296.4 + 81580.8 = 324138.
Q. No. 15:
In an examination paper of 5 questions, 5% of the candidates answered all of them and 5% none. Of the rest 25% answered only 1 question and 20% answered only 4 questions. If 49/2 % of the entire candidates answered only 2 questions and 200 candidates answered only 3 questions, how many candidates appeared at the examination ?
Answer: B Suppose the total candidates appeared be x. Then, Number of candidates who answered all = 5x/100 Number of candidates who answered none = 5x/100 Remaining = x - 2(5x/100) = 9x/10 Number of candidates answered only 1 question = 25% of 9x/10 = 9x/40. Number of candidates answered 4 question = 9x/10 * 20% = 9x/50 Candidate who answered two questions = 49/2 % of x = 49x/200 Now, 2(5x/100) + 9x/40 + 9x/50 + 49x/200 = x By solving this, we get x = 800. Hence, number of candidates appeared = 800.
Q. No. 16:
Of the 50 researchers in a workgroup, 40% will be assigned to team A and the remaining 60% to team B. However, 70% of the researchers prefer team A and 30% prefer team B. What is the least possible number of researchers who will not be assigned to the team they prefer ?
Answer: D Number of researchers prefer team A = 50 * 70/100 = 35. Researchers assigned to A = 50 * 40/100 = 20 Difference = 15. Prefer team B = 50 * 30/100 = 15 Assigned to B = 50 * 60/100 = 30 Difference = 15. Hence, least possible number of researchers who will not be assigned to the team they prefer = 15+15 = 30.
Q. No. 17:
A survey shows that 61%, 46% and 29% of the people watched '3 idiots', 'Rajneeti' and 'Avtaar' respectively. 25% people watched exactly two of the three movies and 3% watched none. What percentage of people watched all the three movies ?
In 2006, Raveendra was allotted 650 shares of Sun Systems Ltd in the initial public offer, at the face value of Rs 10 per share, In 2007, Sun Systems declared a bonus at the rate of 3:13. In 2008, the company again declared the bonus at the rate of 2:4. In 2009, the declared the dividend of 12.5%. How much dividend does Raveendra get in 2009 as the percentage of his initial investment ?
Answer: D Bonus share of sun system Ltd. received by Raveendra in 2007 = 650 * 3/13 = 150 Total = 650+150 = 800 And, In 2008 it is 800 * 1/2 = 400 Total = 800+400 = 1200 In 2009, when bonus share were announced he has 550 share additionally, Percentage = 1200*12.5*100/650 = 23%.