Mathematics Model Practice Questions for

RRB Loco Pilot (ALP) Examination 1. If *381 is divisible by 11, then the digit at tae place of * is

(a) 0 (b) 1 (c) 4 (d) 7

2. By which smallest number should 5808 be multiplied so that it becomes a perfect square?

(a) 2 (b) 7 (c) 11 (d) 3

3. The least number which when divided by 4, 6, 8, 12 and 16 leaves a remainder of 2 in each case is

(a) 46 (b) 48 (c) 50 (d) 56

4. Sum of two numbers is 40 and their product is 375. What will be the sum of their reciprocals?

5. The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers ?

(a) 8 and 6 (b) 8 and 10 (c) 2 and 4 (d) 6 and 4

6. In a class 3/5 of the students are girls and rest are boys. If 2/9 of the girls 1/4 and of the boys are absent. What part of the total number of students are present?

7. Two numbers differ by 5. If their product is 336, the sum of the two numbers is

(a) 21 (b) 28 (c) 37 (d) 51

8. The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets same number of pens and. same number of pencils, is:

(a) 91 (b) 910 (c) 1001 (d) 1911

9. Unit digit in (264)102 + (264)103 is:

(a) 0 (b) 4 (c) 6 (d) 8

10. Which one of the following is the least?

Answer: 1. (d) 2. (d) 3. (c) 4. (a) 5. (d) 6. (a) 7. (c) 8.(a) 9. (a) 10. (d)

1. A person who spends of his income is able to save Rs. 1,200 per month. His monthly expenses (in Rs) is:

(a) 1,200 (b) 2,400 (c) 3,000 (d) 3,200

2. If 80% of A = 50% of B and B = x% of A, then the value of x is:

(a) 400 (b) 300 (c) 160 (d) 150

3. If x is 80% of y, what percent of x is y?

(a) 75% (b) 80% (c) 100% (d) 125%

4. In a town, the population was 8000. In one year, male population increased by 10% and female population increased by 8% but the total population increased by 9%. The number of males in the town was

(a) 4000 (b) 4500 (c) 5000 (d) 6000

5. In an examination, there were 1000 boys and 800 girls. 60% of the boys and 50% of the girls passed. Find the percent of the candidates failed?

(a) 46.4 (b) 48.4 (c) 44.4 (d) 49.6

6. If A exceeds B by 40%, B is less than C by 20%, then A C is,:

(a) 28 : 25 (b) 26 : 25 (c) 3 : 2 (d) 3 : 1

7. Price of sugar rises by 20%. By how much percent should the consumption of sugar be reduced so that the expenditure does not change?

(a) 20 (b) 10

(d) 15

8. In a school 70% of the students are girls. The number of boys are 510. Then the total number of students in the school is

(a) 850 (b) 1700 (c) 1830 (d) 1900

9. Applied to a bill for Rs. 1,00,000 the difference between a discount of 40% and two successive discounts of 36% and 4% is

(a) Nil (b) Rs. 1,440 (c) Rs. 2,500 (d) Rs. 4,000

10. A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price, how much profit or loss does he make, if any?

(a) 1% gain (b) 1% loss (c) 5% gain (d) No gain, no loss

Answer: 1. (b) 2. (c) 3. (d) 4. (a) 5. (c) 6. (a) 7. (c) 8. (b) 9. (b) 10. (b)

1. The area of a circle is 38.5 sq. cm. Its circumference (in cm) is (a) 22 (b) 24 (c) 26 (d) 32 2. The breadth of a rectangular hall is three-fourths of its length. If the area of the floor is 768 sq. m. then the difference between the length and breadth of the hall is (a) 8 metres (b) 12 metres (c) 24 metres (d) 32 metres 3. A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then (a) H = 2R

(d) B = 3R 4. A conical vessle whose internal radius is 12 cm and height 50 cm is full of liquid. The contents are emptied into a cylindrical vessel with radius (internal) 10 cm. The height to which the liquid rises in the cylindrical vessel is (a) 25cm (b) 20cm (c) 24cm (d) 22cm 5. Two right circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is

(b) 2 : 1 (c) 1 : 2 (d) 1 : 4

6. A and B can do a work in 12 days. B and C in 15 days. C and A in 20 days. If A, B and C work together, they will complete the work in: (a) 5 days

(c) 10 days

7. A is thrice as good a workman as B and therefore, able to finish a job in 60 days less than B. Working together they will do it in: (a) 20 days

(c) 25 days (d) 30 days 8. Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is: (a) 50 minutes (b) 12 minutes (c) 25 minutes (d) 15 minutes 9. If 6 men and 8 boys can do a piece of work in 10 days and 266 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys to do the same type of work will be: (a) 5 days (b) 4 days (c) 6 days (d) 7 days 10. A and B can do a work in 18 and 24 days respectively. They worked together for 8 days and then A left. The remaining work was finished by B in: (a) 5 days

(c) 8 days (d) 10 days

Answer: 1. (a) 2. (a) 3. (a) 4. (c) 5. (a) 6. (c) 7. (b) 8. (b) 9. (b) 10. (b)

1. If a man walks 20 km at 5 km/hr, he will be late by 40 minutes. If he walks at 8 km per hr, how early from the fixed time will he reach?

(a) 15 minutes (b) 25 minutes (c) 50 minutes

2. A boy rides his bicycle 10km at an average speed of 12 km per hr and again travels 12 km at an average speed of 10 km per hr His average speed for the entire trip is approximately: (a) 10.4km/hr (b) 10.8 km/hr (c) 11.0 km/hr (d) 12.2 km/hr 3. A train 180 m long moving at the speed of 20 m/sec. over-takes a man moving at a speed of 10m/sec in the same direction. The train passes the man in (a) 6 sec (b) 9 sec (c) 18 sec (d) 27 sec 4. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/ hr Another train starts from B at 9 a.m. and travels towards A at 75 km/hr At what time do they meet? (a) 10 a.m. (b) 10 : 30 a.m. (c) 11 a.m. (d) 11 : 30 a.m. 5. In covering a certain distance, the speeds of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is (a) 1 hour

(c) 2 hours

Directions : A survey of film watching habits of people living in 5 cities, I, II, III, IV and V is summarised below. The column (a) gives percentage of film-watchers in each city who see only film a week. The column (b) gives the total number of film-watchers who see more than one film per week. Read the table and answer question 115 and 120: City (a) (b) I 50 3200 II 30 3500 III 65 7000 IV 25 5400 V 80 2900 6. How many film-watchers in city II see only one film a week? (a) 900 (b) 1500 (c) 1600 (d) 3200 7. Which city has the highest number of film-watchers who see only one film a week? (a) I (b) II (c) III (d) IV 8. The city with the lowest number of film-watcher is (a) I (b) II (c) IV (d) V 9. The city with the highest number of film-watchers is (a) I (b) V (c) IV (d) III 10. The total number of all filmwatchers in the five cities who see only one film a week is (a) 31100 (b) 29500

(c) 28600 (d) 28300

Answer: 1. (c) 2. (b) 3. (c) 4. (c) 5. (c) 6. (b) 7. (c) 8. (b) 9. (d) 10. (a) 1. If a sum of money at simple interest doubles in 12 years, the rate of interest per annum is

(b)7.5%

(d)10% 2. 0.6 of a number is equal to 0.08 of another number. The ratio of the numbers will be (a) 3 : 4 (b) 4 : 3 (c) 2 : 15 (d) 2 : 9 3. 1/5 of a number exceeds 1/7 of the same number by 10. The number is : (a) 125 (b) 150 (c) 175 (d) 200 4. A boys was asked to find the value of 3/8 of a sum of money. Instead of multiplying the sum by 3/8 he divided it by 3/8 and then his answer exceeded by Rs. 55. Find the correct answer? (a) Rs. 9 (b) Rs. 24 (c) Rs. 64 (d) Rs. 1,320 5. The sum of three consecutive odd natural numbers each divisible by 3 is 72. What is the largest among them? (a) 21 (b) 24 (c) 27 (d) 36

Directions: Questions are based on the following bar graph. Read the graph and answer the questions. 6. What is the percentage increase in the gross traffic receipts in 1995-96 as compared to 1993-94? (a) 33.9% (b) 41.5% (c) 20.7% (d) 17% 7. If profit = gross traffic receipts – total expenditure, then in 1996-97, what percentage of gross traffic receipts is the profit made? (a) 5.9% (b) 6.4% (c) 7.2% (d) 8% 8. In which year was the profit as a percentage of gross traffic receipts the highest? (a) 1997-98 (b) 1996-97 (c) 1995-96 (d) 1994-95 9. In order to make a profit of 10%. What should have been the gross traffic receipts (in Rs. crores) in 1994-95, total expenditure remaining the same? (a) 5,667 (b) 5,876 (c) 6,444 (d) 7,667 10. By what amount (in Rs. crores) has the expenditure increased over the period 1993-94 to 1997-98? (a) 4,100 (b) 3,900 (c) 3,850 (d) 3,700

Answer: 1. (c) 2. (c) 3. (c) 4. (b) 5. (c) 6. (b) 7. (a) 8. (d) 9. (c) 10. (d)

1. The area of a sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm is

(a) 8.5 cm2 (b) 8.75 cm2 (c) 7.75 cm2 (d) 7.50 cm2

2. A man buys 12 articles for Rs. 12/- and sells them at the rate of Rs. 1.25 per article. His gain percentage is

(a) 20 (b) 25 (c) 15 (d) 18 3. The cost price of 15 articles is same as the selling price of 10 articles. The profit per cent is:

(a) 30% (b) 40% (c) 50% (d) 45% 4. By selling an article for Rs. 240, a man incurrs a loss of 10%. At what price should he sell it, so that he makes a profit of 20% ? (a) Rs. 264 (b) Rs. 288 (c) Rs. 300 (d) Rs. 320 5. A house and a shop were sold for Rs. 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale into 20% profit. The entire transaction resulted in (a) no loss no gain (b) gain of Rs. lakh (c) loss of Rs. lakh (d) loss of Rs. lakh

6. If a man estimates his loss as 20% of the selling price, then his loss per cent is (a) 20% (b) 25%

(d) Data inadequate

7. If , is equal to (a) 3: 2: 1 (b) 1: 2: 6 (c) 1: 3: 6 (d) 2: 4: 6 8. Divide Rs. 1250 among A, B, C, so that A gets of B’s share and C gets 4 of A’s share. (a) Rs. 200, Rs. 800, Rs. 250 (b) Rs. 200, Rs. 900, Rs. 150 (c) Rs. 150, Rs. 800, Rs. 300 (d) Rs. 200, Rs. 900, Rs. 75 9. The ratio of two numbers is 3 : 8 and their difference is 115. The smaller of the two numbers is (a) 184 (b) 194 (c) 69 (d) 59 10. Between two consecutive years my incomes are in the ratio of 2 : 3 and expenses in the ratio 5 : 9. If my income in the second year is Rs. 45000 and my expenses in the first year is Rs. 25000 my total savings for the two years is

(a) Nil (b) Rs. 15000 (c) Rs. 10000 (d) Rs. 5000

Answer: 1. (b) 2. (b) 3. (c) 4. (d) 5. (c) 6. (d) 7. (b) 8. (b) 9. (c) 10. (d) 1. Rs. 180 contained in a box consists of one rupee, 50 paise and 25 paise coins in the ratio 2 : 3 : 4. What is the number of 50 paise coins? (a) 60 (b) 120 (c) 150 (d) 180

2. Of the three numbers whose average is 60, the first is one fourth of the sum of the others. The first number is (a) 30 (b) 36 (c) 42 (d) 45 3. The average of 11 numbers is 10.8. If the average of the first six be 10.4 and that of the last six is 11.5, then the middle (6th) number is (a) 10.3 (b) 12.6 (c) 13.5 (d) 15.5 4. The average age of 12 players of a team is 25 years. If the captain’s age is included, the average age increases by 1 year. The age of the captain is : (a) 25 yrs. (b) 38 yrs. (c) 36 yrs. (d) 26 yrs. 5. The average income of 40 persons is Rs. 4200 and that of another 35 persons is Rs. 4000. The average income of the whole group is: (a) Rs. 4100 (b) Rs. 4106 3 (c) Rs. 410623 (d) Rs. 4108 3

6. The length of the diagonal of a square is ‘a’ cm. Which of the following represents the area of the square (in sq. cm.) ? (a) 2a

(c) a2/2 (d) a2/4 7. If the volumes of two cubes are in the ratio 27: 1, the ratio of their edges is (a) 3 : 1 (b) 27 : 1

(c) 1 :3 (d) 1 : 27 8. The sides of a rectangular plot are in the ratio 5:4 and its area is equal to 500 sq.m. The perimeter of the plot is (a) 80m. (b) 100m. (c) 90m. (d) 95m. 9. The radius of a wheel is 21 cm. How many revolution will it make in travelling 924

metres? (a) 7 (b) 11 (c) 200 (d) 700 10. The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88cm2. The volume of the cuboid is: (a) 120 cm3 (b) 64 cm3 (c) ,48 cm3 (d) 24 cm3

Answer: 1. (b) 2. (b) 3. (b) 4. (b) 5. (c) 6. (c) 7. (a) 8. (c) 9. (d) 10. (c)

1. Find the length of the largest rod that can be placed in

2. A solid metallic cone of height 10 cm, radius of base 20 cm is melted to make spherical balls each of 4 cm. diameter. How many such balls can be made ?

(a) 25 (b) 75

(c) 50 (d) 125 3. The height of a conical tank is 60 cm and the diameter of its base is 64cm. The cost of painting it from outside at the rate of Rs. 35 per sq. m. is (a) Rs. 52.00 approx. (b) Rs. 39.20 approx. (c) Rs. 35.20 approx. (d) Rs. 23.94 approx. 4. A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by :

5. A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ? (a) 80 days (b) 100 days (c) 60 days (d) 150 days

6. The value of (256)0.16 × (256)0.09 is : (a) 256.25 (b) 64 (c) 16 (d) 4

7. Simplify : (a) 1 (b) 0.1 (c) 0.01 (d) 0.001

(a) 1/2 (b) 4 (c) 2 (d) 1/4 9. 1 – [5 – {2 + (–5 + 6 – 2) 2}] is equal to :

(a) –4 (b) 2 (c) 0 (d) –2

10. if then value of x is:

(a) 1.64 (b) 2.64 (c) 1.764 (d) 0.1764

Answer: 1. (c) 2. (d) 3. (d) 4. (d) 5. (c) 6. (d) 7. (c) 8. (c) 9. (a) 10. (d) 1.

(d)916

2. , the value of 8 × 2 is :

(a) 6 (b) 10 (c) 14 (d) 16

3. The square root of

(a) 4 (b) 3 (c) 2 (d) 1

4. Find the value of

(a) 12 (b) 8 (c) 4 (d) –4

5. If 3x + 8 = 272x + 1, the value of x is :

(a) 7

7. If log102 = 0.3010 and log107 = 0.8451, then the value of log102.8 is :

(a) 0.4471 (b) 1.4471 (c) 2.4471 (d) 1.4471

8. Which of the following fractions is the smallest?

9. (49)15 – 1 is exactly divisible by:

(a) 50 (b) 51 (c) 29 (d) 8

10.

Answer: 1. (c) 2. (c) 3. (c) 4. (c) 5. (d) 6. (b) 7. (a) 8. (l) 9. (d) 10. (a) 1. If 1/3 of a tank holds 80 litres of water, then the

(a) 240 litres (b) 120 litres

(d) 100 litres

2. The LCM of two numbers is 495 and their HCF is 5. If the sum of numbers is 100, then their difference is :

(a) 10 (b) 46 (c) 70 (d) 90

3. LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number will be :

1. (c) 2. (c) 3. (c) 4. (c) 5. (d) 6. (b) 7. (a) 8. (l) 9. (d)

1. If 1/3 of a tank holds 80 litres of water, then the quantity of water that 1/2 tank holds is :

2. The LCM of two numbers is 495 and their HCF is 5. If the sum of numbers is 100, then

3. LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number

1. (c) 2. (c) 3. (c) 4. (c) 5. (d) 6. (b) 7. (a) 8. (l) 9. (d)

quantity of water that 1/2 tank holds is :

2. The LCM of two numbers is 495 and their HCF is 5. If the sum of numbers is 100, then

3. LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number

(a) 5 (b) 25 (c) 45 (d) 225

4. 2/3 of three-fourth of a number is:

5. If we write 45 as sum of four numbers so that when 2 is added to first number, 2 subtracted from second number, third multiplied by 2 and fourth divided by 2, we get the same result, then the four numbers are:

(a) 1, 8, 15, 21 (b) 8, 12, 5, 20 (c) 8, 12, 10, 15 (d) 2, 12, 5, 26

6. Four numbers are in the ratio 1 : 2 : 3 : 4. Their sum is 16. The sum of the first and fourth number is equal to :

(a) 5 (b) 8 (c) 10 (d) 80

7. If 3 times a number exceeds its 3/5 by 60, then what is the number?

(a) 25 (b) 35 (c) 45 (d) 60

8. The numerator and denominator of a fraction are in the ratio of 2 : 3. If 6 is subtracted from the numerator, the result is a fraction that has a value 2/3 of the original fraction. The numerator of the original fraction is :

(a) 6 (b) 18

(c) 27 (d) 36

9. The sum of three consecutive odd natural numbers is 147. Then, the middle number is :

(a) 47 (b) 48 (c) 49 (d) 51

10. If 5432*2 is divisible by 9, then the digit in place of * is :

(a) 0 (b) 1 (c) 6 (d) 9

Answer: 1. (b) 2. (a) 3. (c) 4. (a) 5. (b) 6. (b) 7. (l) 8. (b) 9. (c) 10. (c)

1. is equal to : (a) 1 (b) 6

2. A common factor of (137 + 117) and (135 + 115) is :

(a)24 (b) 135 + 115 (c)132 + 112

(d) None of the above

3. If log10 2 = 0.3010 is given, then log2 10 is equal to:

(a) 0.3010 (b) 0.6990

4. The value of is:

(a) 0.02 (b) 0.004

(c) 0.4 (d) 0.04

5. The next number of the sequence 3, 5, 9, 17, 33 ... is:

(a) 65 (b) 60 (c) 50 (d) 49

6. is equal to :

(a)1 (b)2

7. The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.? (a) 24 (b) 48 (c) 56 (d) 60

8. If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is:

(a) 40 (b) 44 (c) 80 (d) 88

9. is equal to:

10.

Answer: 1. (d) 2. (a) 3. (c) 4. (d) 5. (a) 6. (a) 7. (d) 8. (a) 9. (d) 10. (a)

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