Deepak closes his account in an investment scheme by withdrawing Rs 10,000. 1 year ago he had withdrawn Rs 6,000. 2 year ago he had withdrawn Rs 5,000. 3 year ago he had not withdrawn any money. How much money had Deepak deposited approximately at the time of opening the account 4 year ago, if the annual simple interest is 10%?

Answer: B Let x be the money he deposited at the time of opening the account. So, after 1 year (i.e 3 year ago) it would amount to 1.1x. Since no money was withdrawn at this point, after 2 year(i.e 2 year ago) it would amount to 1.21 x At this point, the person withdrawn Rs 5,000. Hence, principal for the next year = 1.21x - 5000 Next year he earns 10% interest on this, which will amount to 1.1(1.21x - 5000) = 1.32 x - 5500 At this point he withdrawn Rs 6,000. Hence his principal for the next year be 1.32x -11500. He earns 10% interest on this, which amounts to 1.1(1.32x-11500) = 1.452 - 12650. But this is equal to 10,000 Hence, x= 15600.

Q. No. 2:

At the end of the year 2002, Rajoria Institute of Management (RIM) had conducted 108 Management Development Programmes (MDP). Henceforth, every year the institute added p% of the MDP topicsat the beginning of the year and discarded q% of the outdated MDP topics at the end of the year,where p < 0 and q > 0. If RIM scheduled 108 MDP programmes at the end of the year 2006, whichone of the following is true?

Answer: C In any given year, the number of program conducted, remain the same. The number ofprogrammes added at the beginning of every year must be equal to the number ofprogrammes that are discarded at the end of every year. We must have: 108 * (p/100) = 108 * (1 + p/100)* q/100 After simplifying we get the relation p = q+ pq/100. Clearly p> q.

Q. No. 3:

At the end of 2006, Imran had 8 dozens of sheeps. After that, at the beginning of every year he increased his flock by a% and at the end of every year he sold b% of his flock. At the end of 2010, after he sold b% of his flock, he was left with 8 dozens of sheeps. If there were no other change in the number of sheeps with Imran during this period, which of the following is true?

Answer: C Number of shepps with him at the end of 2006 after his sales => 8(12)(1+ a/100)(1- b/100). Number of sheeps with him at the end of 2007 after his sales => 96(1 + a/100)^{2}(1 - b/100)^{2} Similarly, the number of sheeps with him at the end of 2010 after his sales => 96(1+a/100)^{4}(1-b/100)^{4} = 96 (Given) (1+a/100)^{4}(1-b/100)^{4} = 1 If x= y it is violated as, (1-(b/100)^{2})^{4} which is less than 1 The above equation is also violated even if a < b. Thus, a > b is the answer.

Q. No. 4:

As Rao paid equated monthly installments (EMI's) of Rs 25,000 each in January and February towards her home loan, whose outstanding principal amount was Rs 10,00,000 in December. Each EMI consists of interest of outstanding loan amount for the month and part payment of the loan amount. If the interest on the loan is 12% per annum (interst is paid monthly on the diminishing outstanding loan) , the total amount of interest that was paid by Mr. Rao in January and February was :

Answer: C Outstanding amount in December = Rs 10,00,000 Interest to be paid in January = 1% of 10,00,000 = Rs 10,000.............(i) (Since 12 % per annum = 1% per month ) past payment = Rs 25,000 - Rs 10,000 = Rs 15,000 Outstanding amount in January = Rs 10,00,000 - Rs 15,000 = Rs 9,85,000 Interest to be paid in February = 1% of 9,85,000 = Rs 9850 .................(ii) Total interest paid = Rs 10,000 + rs 9850 = Rs 19,850.

Q. No. 5:

To start a new enterprise, Mr. Yogesh has borrowed a total of Rs 60,000 from two money lenders with the interest being compounded annually, to be repaid at the end of 2 year. Mr. Yogesh repaid Rs 38,800 more to the first money lender compared to the second money lender at the end of 2 year. The first money lender charged an interest rate, which was 10% more than what was charged by the second money lender. If Mr. Yogesh had instead borrowed Rs 30,000 from each at their respective initial rates for 2 years, he would have paid Rs 7500 more to the first money lender compared to the second. Then, money borrowed by Mr. Yogesh from first money lender is :

Answer: C If the rate of interest changed by the second part is r%. Then, on the first it is (r+10)%. 30,000[1 + (r+10)/100]^{2} - 30000[1 + r/100]^{2} = 7500 r = 20% Let the first part be x , then the second part will be 60,000-x x[1 + 30/100]^{2} - (60,000-x)[1 + 20/100]^{2} = 38,800 => x = 40,000.