Test booklet: प्रश्न पुस्तिका
Booklet No.: 7145850
Series: B

IBPS RRB PO (Officer Scale-I) Prelims Paper 6

Questions: 80
Maximum marks: 80
Minutes allowed: 45

Instructions निर्देश

This booklet has 80 questions in 2 parts: A. Reasoning (40), B. Quantitative Aptitude (40).
Each part has its own clock. When it runs out, that part closes and the next opens.
Each question has 5 options and one right answer. A right answer earns 1 mark. A wrong answer costs 0.25. A question left blank scores nothing.
Fill one bubble per question on the answer sheet. Unlike a real sheet, you can clear it and change your mind.

Scripting is off, so this page is a printed paper: answer on paper, then open each question’s working.

Part BQuantitative Aptitude

40 questions, 1 mark each, 0.25 off for a wrong answer

Solve both equations and compare x and y.
I. x² − x − 42 = 0
II. y² − 19y + 84 = 0

Question 41 x > y x ≥ y x < y x ≤ y x = y or no relation can be established

Answer and working
Answer D
I gives x = −6 or 7. II gives y = 7 or 12. No x is greater than any y, and one value of each is equal: x ≤ y.
The average weight of 5 people goes up by 2.5 kg when a new person takes the place of one who weighs 75 kg. What does the new person weigh?

Question 42 77.5 kg 62.5 kg 87.5 kg 90 kg 85 kg

Answer and working
Answer C
The total rises by 5 × 2.5 = 12.5 kg, so the new person weighs 75 + 12.5 = 87.5 kg.
35 litres of a mixture contains milk and water in the ratio 3 : 2. How much water must be added to make the ratio 1 : 6?

Question 43 112 litres 16 litres 56 litres 114 litres 126 litres

Answer and working
Answer A
Milk = 21 l, water = 14 l. For 1 : 6, water must be 21 × 6/1 = 126 l. Add 126 − 14 = 112 litres.
Which number replaces the question mark? 1, 8, 27, 64, 125, ?

Question 44 215 307 186 216 217

Answer and working
Answer D
The rule: the terms are 1³, 2³, 3³ …. The missing term is 216.
What is the fourth proportional to 11, 15 and 165?

Question 45 1 236 225 169 121

Answer and working
Answer C
11 : 15 = 165 : x, so x = 15 × 165 ÷ 11 = 225.
Find the wrong number in the series: 23, 29, 31, 37, 41, 45, 47

Question 46 31 47 45 29 41

Answer and working
Answer C
The rule: consecutive prime numbers. The term in place of 45 should be 43, so the wrong number is 45.
A boat covers 42 km downstream in 2 hours and 90 km upstream in 6 hours. What is the speed of the stream?

Question 47 4 km/h 18 km/h 3 km/h 5 km/h 6 km/h

Answer and working
Answer C
Downstream speed = 42 ÷ 2 = 21 km/h; upstream = 90 ÷ 6 = 15 km/h. Stream = (21 − 15) ÷ 2 = 3 km/h.
The fare for a journey goes from ₹720 to ₹792. What is the percentage increase?

Question 48 15% increase 9.09% increase 10% increase 5% increase 20% increase

Answer and working
Answer C
Change = ₹72. On the original value: 72 ÷ 720 × 100 = 10%, a 10% increase. Dividing by the new value, 792, is the usual slip.
A is three times as efficient as B. Together they finish a job in 36 days. How long would A take alone?

Question 49 12 days 51 days 48 days 108 days 144 days

Answer and working
Answer C
If B does 1 unit a day, A does 3; together 4 units a day for 36 days = 144 units. A alone: 144 ÷ 3 = 48 days.
Simplify: ³⁄₅ + ¹⁄₂ + ⁷⁄₁₂

Question 50 ¹⁷⁄₁₀ ¹⁰¹⁄₆₀ ¹¹⁄₁₉ ⁵⁄₃ ¹⁰¹⁄₆₁

Answer and working
Answer B
Over the common denominator 60: the sum is ¹⁰¹⁄₆₀. Adding tops and bottoms separately (11/19) is the trap.
Two trains 160 m and 220 m long run on parallel tracks in opposite directions at 31 km/h and 41 km/h. How long do they take to cross each other?

Question 51 19 seconds 18 seconds 38 seconds 68 seconds 21 seconds

Answer and working
Answer A
Relative speed = 31 + 41 = 72 km/h = 20 m/s. Distance = 160 + 220 = 380 m. Time = 380 ÷ 20 = 19 seconds.
A bag holds 4 red, 3 blue and 4 green balls. Two balls are drawn at random without replacement. What is the probability that both are red?

Question 52 ⁴⁄₁₁ ¹²⁄₁₂₁ ⁴⁄₅₅ ⁶⁄₅₅ ¹⁶⁄₁₂₁

Answer and working
Answer D
Ways to pick 2 red: 6. Ways to pick any 2: 55. Probability = ⁶⁄₅₅.
Which number replaces the question mark? 6, 7, 11, 20, 36, 61, ?

Question 53 96 133 86 98 97

Answer and working
Answer E
The rule: the differences are squares: 1, 4, 9, 16, 25, 36. The missing term is 97.
Solve both equations and compare x and y.
I. x² − 15x + 54 = 0
II. y² + 13y + 36 = 0

Question 54 x > y x ≥ y x < y x ≤ y x = y or no relation can be established

Answer and working
Answer A
I gives x = 6 or 9. II gives y = −9 or −4. Every x is greater than every y: x > y.
Solve both equations and compare x and y.
I. x² + 15x + 56 = 0
II. y² − 5y − 50 = 0

Question 55 x > y x ≥ y x < y x ≤ y x = y or no relation can be established

Answer and working
Answer C
I gives x = −8 or −7. II gives y = −5 or 10. Every x is smaller than every y: x < y.
Solve both equations and compare x and y.
I. x² − x − 30 = 0
II. y² − 7y − 60 = 0

Question 56 x > y x ≥ y x < y x ≤ y x = y or no relation can be established

Answer and working
Answer E
I gives x = −5 or 6. II gives y = −5 or 12. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.
Solve both equations and compare x and y.
I. x² − 10x + 21 = 0
II. y² − 16y + 48 = 0

Question 57 x > y x ≥ y x < y x ≤ y x = y or no relation can be established

Answer and working
Answer E
I gives x = 3 or 7. II gives y = 4 or 12. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.
A trader buys a bicycle for ₹1,725 and sells it for ₹1,449. What is the profit or loss percent?

Question 58 16% loss 14% loss 19.05% loss 16% profit 21% loss

Answer and working
Answer A
Loss = ₹276. As a percent of the cost price: 276 ÷ 1,725 × 100 = 16% loss.
Directions for questions 59 to 63
Study the table and answer the questions that follow.
Books issued by five libraries, in two successive years
Library Year 1 Year 2
Library A 680 748
Library B 460 552
Library C 700 630
Library D 640 832
Library E 320 416
What is the total for Library D over the two years?

Question 59 1,472 1,664 1,492 1,388 1,452

Answer and working
Answer A
640 + 832 = 1,472.
What is the ratio of Library E’s Year 1 figure to Library D’s Year 2 figure?

Question 60 1 : 2 5 : 13 13 : 5 13 : 20 85 : 208

Answer and working
Answer B
320 : 832 = 5 : 13.
Library A’s Year 2 figure is what percent of Library E’s Year 2 figure?

Question 61 55.61% 212.5% 189.81% 179.81% 169.81%

Answer and working
Answer D
748 ÷ 416 × 100 = 179.81%.
What is the average Year 2 figure of the five?

Question 62 625.6 560 645.6 597.8 635.6

Answer and working
Answer E
Sum of Year 2 = 3,178. ÷ 5 = 635.6.
By what percent did Library D’s figure change from Year 1 to Year 2?

Question 63 30% increase 35% increase 25% increase 23.08% increase 30% decrease

Answer and working
Answer A
Change = 832 − 640 = 192. On Year 1: 192 ÷ 640 × 100 = 30% increase.
Simplify: ¹⁄₅ + ⁵⁄₈ + ¹⁄₄

Question 64 ²¹⁄₂₀ ⁴³⁄₄₀ ⁷⁄₁₇ ¹¹⁄₁₀ ⁴³⁄₄₁

Answer and working
Answer B
Over the common denominator 40: the sum is ⁴³⁄₄₀. Adding tops and bottoms separately (7/17) is the trap.
What is the difference between the compound interest and the simple interest on ₹11,350 for 2 years at 20% per annum?

Question 65 ₹2,270 ₹454 ₹908 ₹227 ₹4,540

Answer and working
Answer B
For 2 years, CI − SI = P × (R/100)² = 11,350 × (20/100)² = ₹454.
A number is first increased by 10% and then decreased by 50%. What is the net change?

Question 66 35% decrease 40% decrease 45% decrease 5% decrease 45% increase

Answer and working
Answer C
Net effect = 10 − 50 − (10 × 50)/100 = −45%, so 45% decrease.
An article bought for ₹2,650 is sold at a profit of 12%. What is its selling price?

Question 67 ₹2,332 ₹318 ₹2,993 ₹2,662 ₹2,968

Answer and working
Answer E
SP = CP × (100 + profit%)/100 = 2,650 × 112/100 = ₹2,968.
Which number replaces the question mark? 8, 64, 10, 61, 12, 58, 14, ?

Question 68 96 55 56 57 54

Answer and working
Answer B
The rule: two series alternate: 8, 10, 12 … rising by 2, and 64, 61, 58 … falling by 3. The missing term is 55.
Solve both equations and compare x and y.
I. x² − 9x = 0
II. y² − 4y − 21 = 0

Question 69 x > y x ≥ y x < y x ≤ y x = y or no relation can be established

Answer and working
Answer E
I gives x = 0 or 9. II gives y = −3 or 7. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.
What is the value of 84² − 41²?

Question 70 5,475 5,293 15,375 1,849 5,375

Answer and working
Answer E
a² − b² = (a + b)(a − b) = 125 × 43 = 5,375.
What is √144 + √625 − √196?

Question 71 1 21 23 25 24

Answer and working
Answer C
12 + 25 − 14 = 23.
A bus goes from Pune to Nashik at 10 km/h and returns by the same road at 40 km/h. What is its average speed for the whole journey?

Question 72 25 km/h 29 km/h 16 km/h 18 km/h 14 km/h

Answer and working
Answer C
For equal distances, average speed = 2xy/(x + y) = 2 × 10 × 40 ÷ 50 = 16 km/h. The plain average, 25, ignores that the slower leg takes longer.
The sum of the present ages of a father and his son is 88 years. 5 years ago, the father was 5 times as old as the son. How old is the son now?

Question 73 13 years 23 years 15 years 52 years 18 years

Answer and working
Answer E
Let the son be s. Then (88 − s − 5) = 5(s − 5), so 108 = 6s and s = 18 years.
Solve both equations and compare x and y.
I. x² − 20x + 96 = 0
II. y² − y − 56 = 0

Question 74 x > y x ≥ y x < y x ≤ y x = y or no relation can be established

Answer and working
Answer B
I gives x = 8 or 12. II gives y = −7 or 8. No x is smaller than any y, and one value of each is equal: x ≥ y.
Which number replaces the question mark? 4, 5, 9, 18, ?, 59

Question 75 35 34 27 50 33

Answer and working
Answer B
The rule: the differences are squares: 1, 4, 9, 16, 25, 36. The missing term is 34.
Which number replaces the question mark? 8, 14, 21, 29, 38, 48, ?

Question 76 59 60 61 58 70

Answer and working
Answer A
The rule: the differences grow by 1: 6, 7, 8, 9, 10, 11. The missing term is 59.
What is √625 + √784 − √484?

Question 77 29 30 31 19 33

Answer and working
Answer C
25 + 28 − 22 = 31.
A sum of money becomes three times itself in 8 years at simple interest. What is the rate of interest per annum?

Question 78 20% 37.5% 12.5% 25% 27.5%

Answer and working
Answer D
The interest earned is 2 times the principal in 8 years. Rate = 2 × 100 / 8 = 25%.
A shopkeeper marks his goods 20% above the cost price and allows a discount of 10%. What is his profit or loss percent?

Question 79 10% profit 8% profit 30% profit 13% profit 8% loss

Answer and working
Answer B
Take CP = 100. Marked price = 120. After 10% off: 120 × 90/100 = 108. So 8% profit.
What is the value of 57² − 17²?

Question 80 3,060 1,600 2,926 5,328 2,960

Answer and working
Answer E
a² − b² = (a + b)(a − b) = 74 × 40 = 2,960.

Library	Year 1	Year 2
Library A	680	748
Library B	460	552
Library C	700	630
Library D	640	832
Library E	320	416

IBPS RRB PO (Officer Scale-I) Prelims Paper 6

Instructions निर्देश

Part AReasoning

Part BQuantitative Aptitude