__Numerical Ability Practice Questions for IBPS RRB (Set – 5)__**1. In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?**

a) 9 sec

b) 8 sec

c) 7 sec

d) 6 sec

**2. A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?**

a) 3.75 days

b) 4 days

c) 5 days

d) 6 days

e) 7 days

**3. The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass?**

a) 20kg

b) 35kg

c) 55kg

d) 14kg

e) 42kg

**4. A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?**

a) 7kmph

b) 5kmph

c) 3kmph

d) 2.5kmph

e) 6kmph

**5. The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?**

a) 11.0

b) 11.2

c) 11.3

d) 11.4

e) 11.5

**Directions (6 – 10): In each of these questions, two equations (I) and (II) are given. Solve both the equations and give answer**

**a) if x > y**

**b) if x < y**

**c) if x ≥ y**

**d) if x ≤ y**

**e) if x = y or no relation can be established between ‘x’ and ‘y’.**

**6.**

**I. 63x -194 √x +143 = 0; II. 99y - 255 √y +150 = 0**

**7.**

**I. x - 7 √(3x) + 36 = 0; II. y -12 √(2y) + 70 = 0**

**8.**

**I. x^2 - 7 √7x + 84 = 0; II. y^2 - 5 √5y + 30 = 0**

**9.**

**I. 16x^2 – 40x – 39 = 0; II. 12y^2 – 113y + 255 = 0**

**10.**

**I. 6x^2 + 13x = 12 – x; II. 1 + 2y^2 = 2y + 5y/6**

**Solutions:**

**1. D)**T = 60/36 * 18/5 = 6 sec

**2. A)**1/6 + 1/10 = 8/30 = 4/15

15/4 = 3.75 days

**3. B)**7/20 * 100 = 35

**4. D)**100 --- 10 DS = 10

? ---- 1

75 ---- 15
US = 5

? ----- 1
S = (10 - 5)/2

= 2 2 ½ kmph

**5. D)**1 to 11 = 11 * 10.9 = 119.9

1 to 6 = 6 * 10.5 = 63

6 to 11 = 6 * 11.4 = 68.4

63 + 68.4 = 131.4 – 119.9 = 11.5

6th number = 11.5

**6. E)**ReI. 63x -194 √x +143 = 0

or 63x -117 √x - 77 √x +143 = 0

or (7 √x -13)(9 √x -11) = 0

x = 169/49, 121/81

II. 99y - 255 √y +150 = 0

or 99y - 90 √y -165 √y +150 = 0

or (11 √y -10)(9 √y -15) = 0

y = 100/121, 225/81

Therefore relation cannot be established between x
and y.

**7. B)**I. x - 7 √(3x) + 36 = 0

or x - 7 √3. √x + 36 = 0

or x - 3 √3 √x - 4 √3 √x + 36 = 0

or ( √x - 3 √3)(√ x - 4 √3) = 0

x = 27, 48

II. y - 5 √(2y) - 7 √(2y) + 70 = 0

or y - 5 √2 √y - 7 √2 √y + 70 = 0

or ( y - 5 √2)( y - 7 √2) = 0

y = 50, 98

x < y

**8. A)**I. x^2 - 7 √7x + 84 = 0

or (x - 4 √7)(x - 3 √7) = 0

x = 4 √7, 3 √7

II. y^2 - 5 √5y + 30 = 0

or (y - 2 √5)(y - 3 √5) = 0

y = 2 √5, 3 √5

x > y

**9. B)**I. 16x^2 - 40x - 39 = 0

or 16x^2 - 52x + 12x - 39 = 0

or (4x- 13) (4x + 3)

x = 13/4, -3/4

II. 12y^2 - 113y + 255 = 0

or 12y^2 - 45y - 68y + 255 = 0

or (4y - 15) (3y - 17) = 0

y = 15/4, 17/3

Therefore y > x or, x < y

**10. D)**I. 6x^2 + 14x = 12

3x^2 + 7x – 6 = 0

(x + 3) (3x – 2) = 0

x = – 3, 2/3

II. 1 + 2y^2 = 17y / 6

12y^2 – 17y + 6 = 0

12y^2 – 8y – 9y + 6 = 0

4y (3y – 2) – 3 (3y – 2) = 0

(3y – 2) (4y – 3) = 0

y = 2/3, 3/4

Hence, y ≥ x