# Rukmini Railway Group-D Mathematics Vol-1

## Rukmini Railway Group-D Mathematics Vol-1

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### Topic Related posts

MATH TOPICS

1. Algebra.
2. Arithmetic.
3. Calculus.
4. Geometry.
5. Probability and Statistics.
6. Number System.
7. Set Theory.
8. Trigonometry.
9. Number System
10. H.C.F & L.C.M
11. Decimal Fraction
12. Simplification
13. Square Root & Cube Root
14. Average
15. Problem on Numbers
16. Problem on Ages
17. Surds & Indices
18. Percentage
19. Profit & Loss
20. Ratio & Proportion
21. Partnership
22. Compound Proportion
23. Time & Work
24. Pipes & Cistern
25. Time And Distance
26. Problem on train
27. Boats & Streams
28. Allegation & Mixture
29. Simple Interest
30. Compound Interest
31. Area
32. Volume of Solids
33. Races
34. Calendar
35. Clock
36. Stock & Shares
37. True Discount
38. Algebra
39. Banker’s Discount
40. Linear Education in Two Variables
42. Trigonometry
43. Line & Angles
44. Triangles
46. Circle
47. Polygons
48.  Number Series

Q1 A right circular cone is cut by 3 planes parallel to its base. The planes cut the altitude of the cone in four equal parts. Find out the ratio of volume of each part.
A
1 : 7 : 19: 37
B
1 : 8 : 27: 64
C
1: 9 : 16: 25
D
1 : 2 : 3 : 4
» Explain it
Correct Option: A

Volume of cone, V ∝r3 ∝h3

The volume of 1st part, an ∝ h3

Volume of 2nd part, b ∝ 8h3– h3 = 7h3

Volume of 3rd part, c∝ 27h3– 8h3 =19h3

Volume of 4th part, d ∝ 64h3– 27h3 = 37h3

Therefore, required ratio = h3 ∶ 7h3 ∶ 19h3 ∶ 37h3 = 1 ∶ 7 ∶ 19 ∶ 37

Hence, option A is correct.

Q2 -A merchant uses a weight of 125 grams instead of 100 grams while buying an article. He used 80 grams instead of 100 grams while selling. He marked up the price by 20% and then offers 20% discount. Find the overall profit or loss percentage.
A
20%
B
30%
C
40%
D
50%
» Explain it
Correct Option: D
Effective ratio of SP to CP

= 125 × 100 × 120 × 80 = 3
100 80 100 100 2
Therefore Profit Percentage = 1 ×100 = 50 %
2
Thus , D is the correct answer.

3 -If x =
√5 + 1 ,
√5 – 1
then the value of 5×2 – 5x – 1 will be
A
0
B
3
C
4
D
5
» Explain it
Correct Option: C
According to the given question

we have,

x =
√5 + 1 =
√5 + 1
√5 – 1
√5 – 1
Now, Numerator and denominator multiplied by (√5 + 1)

x =
(√5 + 1) × (√5 + 1)
(√5 – 1) (√5 + 1) =
(√5 + 1)2
5 – 1 = √5 + 1
2
Now we also have, 5×2 – 5x – 1

put value of x in above equation

⇒ 5 ( √5 + 1 ) 2 – 5 ( √5 + 1 ) – 1
2 2
⇒ 5 (6 + 2√5) – 5√5 – 5 – 1
4 2
⇒ 5 (3 + √5) – 5√5 – 5 – 2
2 2
⇒ 15 + 5√5 – 5√5 – 7 = 8 = 4
2 2
Hence, option C is correct.

Q4 The ratio of the work done by 50 women to the work done by 25 men, in the same time is 4 : 3. If 18 women and 12 men can finish a piece of work in 5 days, then how many women can finish the same work in 20/3 days?
A
18
B
27
C
33
D
30
» Explain it
Correct Option: B
Given that,

The ratio of the work done by 50 women and 25 men is

1 : 1
3 4
The ratio of the work done by one man and one woman
= 1 : 1
150 100
Let the time taken by one woman and one man to complete the work be 150x and 100x respectively.
18 × 5 + 12 × 5 = 1
150x 100x
x = 6
Q5 Time taken by one woman and one man to complete the work be 180 days and 120 days respectively.

The number of women worked for 20/3 days to complete the work
= 3 × 180 = 27
20
Hence, option B is correct.

## Rukmini Railway Group-D Mathematics Vol-1

Q6 Two varieties of sugar are mixed in the ratio 3 : 2 and sold for ₹80 per kg to make a profit of 25%. If the cost of the variety of sugar whose quantity is more is ₹40 per kg, what is the cost of the other variety of sugar?
A
Rs. 50
B
Rs. 48
C
Rs. 75
D
Rs. 100
» Explain it
Correct Option: D
Sale price of the mixture = Rs.80

Cost price of mixture = 80 × 100 = Rs. 64
125
Rs. 40 Rs. x
\ /
Rs. 64
/ \
x – 64 24
⇒ x – 64 = 3 ⇒ x = Rs. 100
24 2
Hence, option D is correct.

In math questions answers each question are solved with an explanation. The questions are based on different topics. Care has been taken to solve the questions in such a way that students can understand each and every step.

1. Which is greater than 4?

(a) 5,

(b) -5,

(c) -1/2,

(d) -25.
Solution: 5 greater than 4.

2. Which is the smallest?

(a) -1,

(b) -1/2,

(c) 0,

(d) 3.

Solution:

The smallest number is -1.

Q 3. Combine terms: 12a + 26b -4b – 16a.

(a) 4a + 22b,

(b) -28a + 30b,

(c) -4a + 22b,

(d) 28a + 30b.
Solution:

12a + 26b -4b – 16a.

= 12a – 16a + 26b – 4b.

= -4a + 22b.

Q4. Simplify: (4 – 5) – (13 – 18 + 2).

(a) -1,

(b) –2,

(c) 1,

(d) 2.
Solution:

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.

Q5. What is |-26|?

(a) -26,

(b) 26,

(c) 0,

(d) 1
Solution:

|-26|

= 26.

Q6. Multiply: (x – 4)(x + 5)

(a) x2 + 5x – 20,

(b) x2 – 4x – 20,

(c) x2 – x – 20,

(d) x2 + x – 20.
Solution:

(x – 4)(x + 5).

= x(x + 5) -4(x + 5).

= x2 + 5x – 4x – 20.

= x2 + x – 20.

Q7. Factor: 5x2 – 15x – 20.

(a) 5(x-4)(x+1),

(b) -2(x-4)(x+5),

(c) -5(x+4)(x-1),

(d) 5(x+4)(x+1).
Solution:

5x2 – 15x – 20.

= 5(x2 – 3x – 4).

= 5(x2 – 4x + x – 4).

= 5{x(x – 4) +1(x – 4)}.

= 5(x-4)(x+1).

Q8. Factor: 3y(x – 3) -2(x – 3).

(a) (x – 3)(x – 3),

(b) (x – 3)2,

(c) (x – 3)(3y – 2),

(d) 3y(x – 3).

Solution:

3y(x – 3) -2(x – 3).

= (x – 3)(3y – 2).

Q9. Solve for x: 2x – y = (3/4)x + 6.

(a) (y + 6)/5,

(b) 4(y + 6)/5,

(c) (y + 6),

(d) 4(y – 6)/5.
Solution:

2x – y = (3/4)x + 6.

or, 2x – (3/4)x = y + 6.

or, (8x -3x)/4 = y + 6.

or, 5x/4 = y + 6.

or, 5x = 4(y + 6).

or, 5x = 4y + 24.

or, x = (4y + 24)/5.

Therefore, x = 4(y + 6)/5.

Q10. Simplify:(4x2 – 2x) – (-5x2 – 8x).
Solution:

(4x2 – 2x) – (-5x2 – 8x)

= 4x2 – 2x + 5x2 + 8x.

= 4x2 + 5x2 – 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

Q11. Find the value of 3 + 2 • (8 – 3)

(a) 25,

(b) 13,

(c) 17,

(d) 24,

(e) 15.
Solution:

3 + 2 • (8 – 3)

= 3 + 2 (5)

= 3 + 2 × 5

= 3 + 10

= 13

Q12. Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?
Solution:

33/4 ÷ 4 pounds.

= (4 × 3 + 3)/4 ÷ 4 pounds.

= 15/4 ÷ 4 pounds.

= 15/4 × 1/4 pounds.

= 15/16 pounds.

Now we know that, 1 pound = 16 ounces.

Therefore, 15/16 pounds = 15/16 × 16 ounces.

= 15 ounces.