QUANTITATIVE APTITUDE

QUANTITATIVE APTITUDE Questions asked in MIB Examination. If a b 0, then (a b ) ab is equal to: (D) 9. If x y 0, then x y is equal to: y x xy 7 (D). If ab b a 0, then the value of a b b a ab is equal to: ab ab (D) 0 a. If a b, then is equal to: a b 0 (D). If x a b, y b a, ab, then the value of ( a b )( x y ) ax by (D) 0 6. The differene between ompound interest and simple interest for years at % per annum an be found out by multiplying the prinipal by:.76 0.76 0.076 (D) 0.0076 7. The simple interest on a sum of money is 9 th of the sum and the number of years and the rate per ent per annum are equal. The rate per ent per annum 6 (D) 0 8. A man invested Rs,000 at some rate of simple interest and Rs,000 at % higher rate of interest. If the interest in both the ases after years is same the rate of interest in the former ase % % 6 % (D) 8 % 9. A sum of money at simple interest rate amounts to Rs,0 in years and to Rs,0 in 6 years at the same rate of interest. Find the sum and the rate of interest per annum. Rs,00, 6% Rs,000, % Rs,00, % (D) Rs,00, % 0. In how many years, will a sum of Rs 800 at 0% per annum ompound interest semi-annually beome Rs 96.0? (D). On a ertain map of India the atual distane of 0 kms between two ities Delhi and olkata is shown as ms. What sale is used to draw the map? : 0 6 : 0 0 6 : 0 6 (D) : 9 0 6. The ratio between the third proportional of and 0 and mean proportional of 9 and : : 7 : (D) 9 :. mangoes and oranges ost as muh as mangoes and 7 oranges. What is the ratio of ost of one mango to the ost of one orange? : : : (D) :. Rs,00 are divided among P, Q and R. The share of P is of the ombined share of Q and R. P gets: Rs 0 Rs 00 Rs 00 (D) Rs 0 ma n. If a : b : d, then is equal to: mb nd an : mb m : n a : b (D) dm : n 6. How many even numbers of four-digits an be formed with digits,,,,, 6 (repetition of the digit is allowed)? 8 JANUARY 00 THE COMPETITION MASTER

68 80 96 (D) 0 7. In how many ways MBA students and 6 law students an be arranged together so that no two MBA students are side by side? 76!!! 6!.6!!6! (D) P 8. There is a number lok with four rings. How many attempts at the maximum would have to be made before getting the right number? 0 0 (D) 6 9. There are four letters and four envelops addressed to different persons. In how many ways an wrong hoies be made? 6 6 (D) 0. There are 0 points on a straight line AB and 8 points on another AC, none of them being A. How many triangles an be formed with these points as verties? 70 60 86 (D) 680. In a village onsisting of p persons, x% an read and write. Of the male alone y% and of the females alone % an read and write. Find the number of males in the village in terms of p, x, y and, if < y: px ( ) px ( ) ( y x ) ( y x ) py ( x) px ( ) (D) x y. The prie of a ommodity is first inreased by x% and then dereased by x%. If the new prie is, find the original prie from the given below: ( x ) ( x ) ( x ) (D) ( x ). A fration is suh that if the double of the numerator and the triple of the denominator is hanged by 0% and 0% respetively, then we get % of 6. Find fration:. A redits % of his salary in his fixed aount and spends 0% of the remaining on groeries. If the ash in hand is Rs,80, what is his salary? Rs,000 Rs,00 Rs,000 (D) Rs,00 Diretions (Q. Nos. to 8): Read the following and answer the questions that follow: Two friends Shyam and ailash own two versions of a ar. Shyam owns the diesel version while ailash owns petrol version. ailash s ar gives an average that is 0% higher than Shyam s (in terms of litres per kilometre). It is known that petrol osts 60% of its prie higher than diesel.. The ratio of ost per kilometre of ailash s ar to Shyam s ar : :.9 : 6. Shyam s ar gives an average of 0 km per litre, then the differene in the ost of travel per kilometre between the two ars Rs. Rs. Rs. 7. For the above question (6), the ratio of the osts per kilometre of the Shyam s travel to ailash s travel : : :.9 8. Diesel osts Rs. per litre, then the differene in the ost of travel per kilometre between ailash s and Shyam s is (assume an average of 0 km per litre for Shyam s ar and also assume that petrol is 0% of its own prie higher than diesel): Rs.7 Rs 0.87 Rs. 9. A shopkeeper gives onseutive disounts of 0%, % and % after whih he sells his goods at a perentage profit of 0.0% on the ost prie. Find the value of the perentage profit that the shopkeeper would have earned if he had given disounts of 0% and % only: % 6.% 7.% (D) 68.6% 0. A journey of 9 kms takes hours less by a fast train than by a slow train. If the average speed of the slow train is 6 kmph less than that of a fast train, what is the average speed of the fast train? 0 kmph 8 kmph 0 kmph (D) kmph. Two planes move along a irle of irumferene. kms with onstant speeds. When they move in different diretions, they meet every seonds and when they move in the same diretion one plane overtakes the other every 60 seonds. Find the speed of the slower plane: 0.0 km/s 0.0 km/s 0.0 km/s (D) 0.0 km/s. The distane between two towns is x km. A ar travelling between the towns overs the first k km at an average speed of y kmph and the remaining distane at kmph. The time taken for the journey 9 JANUARY 00 THE COMPETITION MASTER

k x k ( ) y ky ( k x) k k x y (D) ky (x k). The metro servie has a train going from Mumbai to Pune and Pune to Mumbai every hour. The first one at 6 a.m. The trip from one ity to another takes hours, and all trains travel at the same speed. How many trains will pass while going from Mumbai to Pune, if you start at noon? 8 0 9 (D) Diretions (Q. Nos. to 8): Read the following and answer the questions that follow: A train journey from P to D by an X-express has lasses of fares: (i) tier Rs 00 7 berths per Train has bogie 8 bogies (ii) AC- tier Rs 898 6 berths per Train has bogie bogies (iii) AC- tier berths per Train has Rs,88 bogie bogies (iv) AC-first lass 6 berths per Train has Rs,69 bogie one bogie The distane between P to D is km. Assume the train does not stop at any station unless otherwise indiated. The running ost per kilometre : AC-bogie Rs, non-acbogie Rs 0.. Assuming full oupany, a bogie of whih lass exhibits the highest profit margin? AC- tier AC- tier AC-first lass (D) tier. Assuming full oupany in all the lasses, for a journey between P and D to Delhi, the profit margin (as a perentage of running osts) of the lass showing the lowest profit is approximately: 6% 7% 09% 6. For the above question, the perentage of the total profit that omes out of AC bogie is (approximately): 0% 60% 70% (D) 80% 7. The highest revenue for a journey from P to D will always be generated by: tier AC- tier AC- tier 8. / of a onsignment was sold at a profit of 6% and the rest at a loss of %. If, however, there was an overall profit of Rs 0.00, the value of onsignment was: Rs,60 Rs,860 Rs,00 (D) Rs 8,000 9. A istern is filled by a tap in hours. Due to a leak in its bottom, it takes hour longer to fill. If istern is full, how long will it take to leak to empty it? 7 hours 8 hours hours (D) 8 hours 0. A an do a piee of work in 7 days of 9 hours eah whereas B an do the same work in 6 days of 7 hours eah. How long will it take to omplete the work together working 8 hours a day? days days 7 days (D) days. If men and 6 boys an do a piee of work in days and men and boys an do it in days, the ratio of daily work done by a man to that done by a boy : : : (D) :. A bus left Delhi for Ambala at 0 km/hr and turned over the same route at 0 km/hr. Thus it took hour more on the return trip. The distane between Delhi and Ambala 00 kms 80 kms 00 kms. A train running at 7 kms per hour rosses a oonut tree standing by the side of the trak in 7 seonds. The length of the train 0 metres 0 metres 0 metres (D) 0 metres. A man purhased a bag of rie ontaining 70 kgs for Rs 7. He sold it at the rate of Rs.7 per kg. Find the profit and loss per ent. 0% profit 0% loss.% profit (D).% loss. If 6% of 0% of a number is 8, the number 00 (D) 0 6. A person marks his goods 0% higher than the ost prie and allows a disount of %. The perentage of profit % 0% % (D) % 0 JANUARY 00 THE COMPETITION MASTER

. Q a b 0 a b ab or (a b ) ab x y. x y xy y x xy xy xy (Q x y 0). (D) ab b a 0 b (ab a) a (ab b) ab (b a) Given exp a b b a ab a a ab b ab b b a aa ( b) bb ( a ) ( b a) b a ab ab( a b ) 0 0 ab( a b ). a b or a b (b ) a a b a ( b ) b a ( a ) b b b b ( a b )( x y ). aa ( b) bb ( a) ( ab) ( a b )( x y ) a ab b ab ab ( a b )( x y ) a b ab ( a b )( a b b a ab ) a b ab a b ab a b ab L F NM HG L R S F NM T HG R n 6. (D) P P R T I J P I J O QP U V W O QP P.0076 P 7. 9 P R R R 0 8. 000 x 000 (x ) x 9. I for years Rs 0 0 Rs ANSWERS AND EXPLANATIONS A P I P 0 Rs 00 R 00 0 0. 96.0 800 ( )n n half years years. (D). Third proportional of and 0 0 7 Mean proportional of 9 and 9 Reqd ratio 7 :. Let the ost of mango be Rs x and that of orange be Rs y ATS x y x 7y x y. Let the ombined share of Q and R be Rs x x x Rs 00 x 70 Share of P 70 Rs 00 a. k a bk, dk b d ma n mbk ndk k a : b mb nd nb nd 6. Unit s plae be filled in ways (i.e. by or or 6) Eah of three remaining plaes (i.e. ten s hundred s and thousand s) an be filled in 6 ways (Q repetition is allowed) Reqd. no. of nos. 6 6 6 68 7. 6 law students an be arranged in 6! ways Now in 7 plaes, MBA students an be arranged in 7 P ways....... Total no. of ways 6! 7 P 6! 7!! 8. 9. (D) 0. 8 C 0 0 C 8 60 [No. of bases on AC 8 C No. of verties on AB 0 No. of s with bases on AC and verties on AB 8 C 0 No. of s with bases on AB and verties on AC 0 C 8]. (D) Total persons who an read and write px JANUARY 00 THE COMPETITION MASTER

Let the no. of males be M A.T.S. M y (p M) px M px ( ) y. (D) Let the original prie be Rs y F xi y J F x k HG HG I J. Let the fration be x y A.T.S. 0 x 70 y k y x 6 x y. Let his salary be Rs x A.T.S. 8 x 70 80 x Rs000. 6. (D) 7. 8. (D) 9. Let CP Rs, P 0.0% S.P. Rs 0.0 Disounts 0%, %, % M.P. 0.0 90 8 8 Rs 00 If disounts are 0% and % only F S.P. M.P. d d 00 90 HG I J F H G I J 8 Rs Profit % 9 0. 9 x Speed of fast train 8 x 6 x. Let the speeds of fast plane and slow planes be x and y m/se respetively D s t If they move in opposite diretion (x y) x y 80 m/se... (i) If they move in same diretion, relative speed x y m/se Time 60 i.e. times Speed is th x y 0 m/se Solving (i) and (ii), y 0 m/se 0.0 km/se. Reqd time k y x k. (D) trains... (ii). (D) tier. (D) 6. 60% 7. tier 8. (D) Let total value of onsignment be Rs x A.T.S. x 06 x 97 x 0 x Rs 8000 9. (D) Tap s hour s work 7 Let the reqd time be x hrs ATS x 8 7 x 0. A s one day s work (by working hour a day) 6 (A B) s one day s work 6 6 (A B) s work by working hours a day 6 Reqd time days. Work done by M 6B in days work done by M B in days 60M 80B M 96 B M B M B : Reqd ratio D D. D 00 km 0 0. Let the length of train be x x 7 x 0 m 7 8. C.P. of 70 kg rie Rs 7 S.P..7 70 8 P 8 7 P% 0 7 6 0. x 8 x 6. (D) Let CP Rs MP Rs 0 S.P. 0 9 Rs P% JANUARY 00 THE COMPETITION MASTER