RRB NTPC Mathematics Test - 1 - RRB NTPC/ASM/CA/TA MCQ

Calculation:

⇒ 10/3 ÷ 45/7 × 3/2 × 22/7 = (p)^1⁄2

⇒ 10/3 × 7/45 × 3/2 × 22/7 = (p)^1⁄2

⇒ (p)^1⁄2 = 2 × 1/9 × 11

⇒ (p)^1⁄2 = 22/9

⇒ p = [22/9]² = 484/81

Therefore, the value of 'p' is 484/81.

Given:

The income ratio of A and B is 5:7

Expenditure ratio is 1:1

A saves Rs. 2000

B saves Rs. 4000

Calculation:

Let's assume the common factor of their incomes is x:

A's income = 5x

B's income = 7x

Since the expenditure ratio is 1:1, and

A and B save Rs. 2000 and Rs. 4000 respectively:

A's expenditure = 5x - 2000

B's expenditure = 7x - 4000

Since the expenditures are equal:

5x - 2000 = 7x - 4000

Now, we'll solve for x:

7x - 5x = 4000 - 2000

2x = 2000

x = 2000 / 2 = 1000

Now, A's income:

A's income = 5 multiplied by 1000 = 5000

So, the income of A is Rs. 5000.

Given:

A sum of ₹ 159250 is divided among A, B, C, and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5, and that of C and D is 2 : 3.

Calculation:

A : B = 1 : 3 = 2 : 6

B : C = 2 : 5 = 6 : 15

C : D = 2 : 3 = 15 : 22.5

So,

A : B : C : D

⇒ 2 : 6 : 15 : 22.5

⇒ 20 : 60 : 150 : 225

⇒ 4 : 12 : 30 : 45

Now, A's share = 159250 × 4/(4 + 12 + 30 + 45)

⇒ 159250 × 4/91 = ₹7000

∴ The share of A is ₹7000 .

Given:

First discount = 10%

Second discount = 15%

Third discount = 20%

Concept Used:

The formula for the equivalent single discount of successive discounts, which is 1 - (1 - d1)(1 - d2)(1 - d3), where d1, d2, d3 are the decimal equivalents of the discounts.

Calculation:

Convert the discounts to decimal form. 10% = 0.1, 15% = 0.15, 20% = 0.2.

The equivalent single discount = 1 - (1 - 0.1)(1 - 0.15)(1 - 0.2) = 1 - (0.9)(0.85)(0.8) = 1 - 0.612 = 0.388.

Percentage = 0.388 × 100% = 38.8%.

Therefore, the equivalent single discount to 10%, 15%, and 20% is 38.8%.

Given

Ratio of two numbers = 2 : 3

HCF = 21

LCM = 126

Concept:

Let the ratio be 2x and 3x, where x is the HCF

Difference of numbers

2x - x = x

since x is the HCF, so x = 21

The difference of these two numbers = 21.

Given:

Distance between policeman and thief = 68 meters.

Speed of policeman & thief = 4 m/s and 9 m/s respectively

Formula Used:

Time taken = Distance/Speed

Relative speed = (a - b) km/hr

Where, a = speed of a policeman & b = speed of a thief

Calculation:

Relative speed = (9 - 4) m/s = 5 m/s

Time taken for the policeman to catch the thief = 68/5 = 13.6 seconds.

Hence, the correct answer is 13.6 seconds.

Given:

A certain sum amounts to Rs. 12,236 in years at 8.8% p.a. at simple interest

Concept used:

S.I = (P × T × R)/100

Here, P = Sum, T = Time & R = Rate

Calculation:

Let the sum be P

According to the question,

[P + (P × 15 × 8.8)/(100 × 4)] = 12236

⇒ P + 0.33P = 12236

⇒ 1.33P = 12236

⇒ P = 12236/1.33

⇒ P = 9200

Now, (9200 × 35 × 8.8)/(8 × 100)

⇒ 92 × 35 × 1.1 = 3542

∴ The simple interest (in Rs.) on the same sum at the same rate in years is 3542.

Formula Used:

Mean of the data (Weighted Mean) = (Σ(X × Y)) / ΣY

Calculation:

Calculate Σ(X × Y) and ΣY:

Σ(X × Y) = (6 × 25) + (3 × 30) + (5 × 40) + (2 × 35) + (4 × 12) + (6 × 26)

Σ(X × Y) = 150 + 90 + 200 + 70 + 48 + 156

Σ(X × Y) = 714

ΣY = 25 + 30 + 40 + 35 + 12 + 26

ΣY = 168

Mean = Σ(X × Y) / ΣY

Mean = 714 / 168

Mean ≈ 4.25

Therefore, the mean of the data given in the table is approximately 4.25.

Given:

The ratio of two numbers = 3 ∶ 4

LCM = 96

Concept used:

LCM or least common multiple is the simplest method to find out the smallest common multiples between two or more than two numbers.

Calculation:

Let the number be 3x, 4x

LCM of (3x and 4x) = 3 × 4 × (x)

⇒ 12x

According to the question,

12x = 96

⇒ x = 96/12

⇒ x = 8

Now,

The difference between the numbers = 4x - 3x

⇒ x

⇒ 8

∴ The difference between the numbers is 8.

∵ AE + EC = AC

⇒ EC = 5 cm

According to angle bisector theorem,

So, AE/EC = AB/BC

⇒ 4/5 = AB/10

∴ AB = 8 cm

Calculation:

Ram + Shyam = 28 × 2 = 56

Rahim + Shyam = 26 × 2 = 52

Rahim + Ram = 30 × 2 = 60

Hence, Ram + Shyam + Rahim = (56 + 60 + 52)/2 = 84

Age of Ram = 84 - 52 = 32 years

Age of Shyam = 84 - 60 = 24 years

Age of Rahim = 84 - 56 = 28 years

∴ Option A is the correct answer.

Given:

B(1995 + 1998) = 1620 + 1600

A(1996 + 1997) = 1590 + 1750

The total number of coolers sold by shopkeeper B in 1995 and 1998 = 1620 + 1600 = 3220

The total number of coolers sold by shopkeeper A in 1996 and 1997 = 1590 + 1750 = 3340

difference = 3220 - 3340 = -120

⇒ less

Required percentage = 120/3340 x 100 = 3.5% ~ 4% less

Hence, the correct option is 2.

Given:

Suresh and Mahesh invested Rs.1,15,000 and Rs.1,85,000 respectively.

Total profit is Rs. 18,000

Concept Used:

Profit is directly proportional to the investment.

Calculation:

The ratio of Suresh and Mahesh investment is,

⇒ 1,15,000: 1,85,000

⇒ 23: 37

Let the profit of Suresh and Mahesh be 23x and 37x

As profit is directly proportional to the investment.

⇒ 23x + 37x = 18,000

⇒ 60x = 18,000

⇒ x = 18,000/60

⇒ x = 300

⇒ Mahesh profit = 37x

⇒ 37 × 300

⇒ 11,100

∴ Mahesh profit is Rs.11,100

Given:

Calculation:

= 1

∴ Option C is the correct answer.

Concept:

Least number divisible by a group of numbers is given by their LCM.

Calculation:

14 = 2 × 7

15 = 5 × 3

18 = 2 × 3²

LCM( 14, 15, 18 ) = 2 × 3² × 5 × 7

LCM( 14, 15, 18 ) = 630

∴ Least number divisible by 14, 15 and 18 is 630

Given:

Principal (P) = Rs.50,000

First rate = 8%; second rate = 12%

Total simple interest (S.I) = Rs.5200

Formula used:

Simple interest (S.I) = (P × R × T)/100

Where P = principal; R = rate; T = time

Calculation:

Let the amount at 12% rate = x

then amount at 8% rate = (50,000 - x)

According to the question:

⇒ (50,000 - x) × 8% + x × 12% = 5200

⇒​ (50,000 × 8%) - (x × 8%) + (x × 12%) = 5200

⇒ (x × 4%) = 5200 - 4000

⇒ x = (1200 × 100)/4 = Rs.30000

∴ The correct answer is Rs.30000.
Shortcut Trick
Calculation:

Overall rate = (5200 × 100)/50000 = 52/5 = 10.4%

Now

Amount at 8% : Amount at 12% = 1.6 : 2.4

⇒ 2 : 3

⇒ 5 units = 50000

⇒ 3 units = (50000 × 3)/5 = Rs.30000

∴ The correct answer is Rs.30000.

Given:

Concept used:
(a + b)² = a² + b² + 2ab
(a² - b²) = (a + b)(a - b)

Calculation:
According to the question,

⇒ ? = 9

Therefore, "9" is the required answer.

Given:
Education = 90% out of 360%
Calculation:
Out of total monthly expenditure, Education = (90/360) × 100 = 25%
∴ The percentage of expenditure on education out of total monthly expenditure is 25%.

Unit digit of 1261 × 3474 × 1269 will be same as unit digit of 1 × 4 × 9

1 × 4 × 9 = 36

Unit digit of 36 is 6

Given:

sin(A + B) = √3/2 and sec(A - B) = 2/√3

Calculation:

We know that Sin60° = √3/2, Sec30° = 2/√3

Sin(A + B) = Sin60°

⇒ (A + B) = 60° ---(1)

Sec(A - B) = Sec30°

⇒ (A - B) = 30°

⇒ A = 30° + B

From equation (1)

⇒ 30° + B + B = 60°

⇒ 2B = 30°

⇒ B = 15°

By solving equation 1, 2 we have

A = 45°, B = 15°

∴ The correct answer is A = 45°, B = 15°

Calculation:

The level of water in the tank rises by 2 cm every minute.

So, between 9:45 am to 9:47 am, the level of the water has risen by 2 cm × 2 = 4 cm.

At 9 : 47 am, height of water was 23 cm, so at 9 : 40 am, 7 min before water level was 23 - (7 × 2) = 23 - 14 = 9 cm

∴ The correct answer is 9 cm

Given:

Numbers: 70, 55, 52, 85, 68, 67, 79

Formula used:

Mean = Sum of all observations / Total number of all observations

There are 'n' observations.

If n is odd, then the median is {(n + 1)/2}th term.

If n is even, then the median is the average of (n/2)th term and {(n/2) + 1}th term.

Calculation:

Mean =

⇒ 476/7 = 68

Arrange all the observations in ascending order.

52, 55, 67, 68, 70, 79, 85

n = 7

So, Median = {(7 + 1)/2}^th term

⇒ 4^th term = 68

Median = 68

The difference between their mean and median = 68 - 68 = 0

∴ The difference between their mean and median is 0.

Train running with 54 kmph crosses a bridge of length 225 meters in 25 seconds

Speed of train in m/s = 54 kmph = 54 × 5/18 m/s = 15 m/s

Let the length of the train be ‘l’ m

⇒ (l + 225)/15 = 25

⇒ l = 150 m

The train completely passes the other train of double its length in 22 seconds

Let the speed of the other train be ‘s’ m/s

⇒ (150 + 300)/(s + 15) = 22

Given:

The areas of two similar triangles are 144 cm² and 196 cm² respectively.

If the longest side of the smaller triangle is 24 cm

Concept Used:

If Two triangle are similar,

Area of two triangle ratio = Square of the longest side ratio

Area of Smaller triangle/Area of Larger triangle = Square of longest side smaller triangle/Square of longest side of larger triangle

Calculation:

According to the question,

Let the longest side of larger triangle be y

Area of Smaller triangle/Area of Larger triangle = Square of longest side smaller triangle/Square of longest side of larger triangle

⇒ 144/196 = (24/y)²

⇒ 24/y = 12/14

⇒ y = 28 cm

∴ The longest side of the larger triangle is 28 cm.

Given:

Numbers: 25, 30 and 60

Calculation:

Factors of 25 = 1 × 5 × 5

Factors of 30 = 1 × 2 × 3 × 5

Factors of 60 = 1 × 2 × 2 × 3 × 5

LCM of 25, 30 and 60 = 1 × 2 × 2 × 3 × 5 × 5 = 300

∴ The LCM of 25, 30 and 60 is 300.

Calculation:
Let the numbers be 2y, 3y and 4y respectively.
⇒ (2y)² + (3y)² + (4y)² = 261
⇒ 29y² = 261
⇒ y² = 9
⇒ y = 3
Greatest number = 4y = 12
Smallest number = 2y = 6
∴ The difference between greatest number and smallest number is 6.

Calculations:
After the first year, the production is:
350 × (1 + 0.08) = 350 × 1.08 = 378
After the second year, the production is:
378 × (1 + 0.05) = 378 × 1.05 = 396.9
After the third year, the production is:
396.9 × (1 + 0.04) = 396.9 × 1.04 = approximately 412.8
So the approximate production after the third year is around 413 (rounded to the nearest whole number).
Hence, The Correct Option is A.

Given

10 years ago, Chris = 3(Alec's age)

Calculation

Let the present age of Chris and Alec be x and y respectively

10 years ago,

x - 10 = 3(y - 10)

⇒ x - 3y = -20 ----(1)

After 10 years

x + 10 = 2(y + 10)

⇒ x - 2y = 10 ----(2)

By solving (1) and (2)

We get x = 70, y = 30

So, the ratio of present age of Chris to Alec = 70 : 30 = 7 : 3

∴ The required answer is 7 : 3

Given:
First 50 natural numbers

Calculation:

First 50 natural numbers are 1, 2, 3,....... 50

Sum of first n natural numbers = [n( n + 1 ) ] / 2

= ( 50 × ( 50 + 1 ) ) / 2 = ( 50 × 51 ) / 2

= 1275

Average = 1275 / 50 = 25.5

∴ The average of first 50 natural numbers is 25.5

Shortcut Trick

The average of first n natural numbers = (n + 1)/2

where, n = 50

⇒ n = (50 + 1)/2 = 51/2 = 13 = 25.5

∴ Average of first 50 natural numbers is 25.5

Given:

Pipe P takes 11 minutes to fill an empty tank and Q can empty it in 33 minutes.

Calculation:

As Q is an empty pipe so the efficiency of Q should be – 1 unit/minute

And The efficiency of P will be 3 unit/minute

Now P & Q can do 2/3 part of the total work in

⇒ Time Taken = {(2/3) × 33}/(3 – 1) = 11 minutes

∴ The time taken by them is 11 minutes