RRB NTPC Mathematics Test - 2 - RRB NTPC/ASM/CA/TA MCQ

Given:
Principal = Rs. 8500
Time = 3 years
Simple Interest = Rs. 2040
Formula used:
Simple Interest = (Principal × Rate × Time)/100
Calculation:
⇒ 2040 = 8500 × Rate/100 × 3
⇒ Rate = 2040/255 = 8
The rate of interest is 8% per annum.

Given:
(1) Total number of students = 5000
(2) Number of students in the Electronics and Communication stream = 20%
(3) The college decided to give ₹300 per student to each stream for the purchase of teaching materials
Calculation:
Number of students in the Electronics and Communication stream = 20%
⇒( 5000 × 20)/100 = 1000
The college decided to give ₹300 per student to
each stream for the purchase of teaching materials.
Total money got by Electronics and Communication stream
⇒ 1000 × 300 = 300000
∴ The required answer is 300000.

Given,

A can do a certain work in = 15 days

A and B can do the same work in = 7.5 days

Concept: / Formula:

Total work = Efficiency × Time Taken

Calculation:

Total work = 15

Efficiency of A and B = 2

Efficiency of A = 1

Let efficiency of B be x, then

⇒ x + 1 = 2

⇒ x = 2 – 1

⇒ x = 1

B alone can complete the whole work in = 15/1 = 15 days

Given,

Let present age of Radha and Ram be a years and b years respectively.

⇒ (a - 6) : (b - 6) = 5 : 8

⇒ 8a - 48 = 5b - 30

⇒ 8a - 5b = 18

Then,

⇒ b - a = 6

Solving,

a = 16 years and b = 22 years

Then,

⇒ (16 + ?) : (22 + ?) = 13 : 16

⇒ 256 + 16? = 286 + 13?

⇒ ? = 10

∴ after 10 years ratio will become 13 : 16.

Total number of votes of all the favourite pizza toppings = 100 + 325 + 200 + 125 + 250 = 1000
Number of votes for pepperoni = 325
Percentage = 325/1000 × 100 = 32.5%
∴ Option D is the correct answer.

Given:

The average of 17 numbers = 55

The average of the first 6 numbers = 49.5

The average of the next 8 numbers = 60.5

16th number = 15th number - 4

16th number = 17th number - 6

Formula Used:

Average = Sum of the observations/Total number of observations

Calculation:

According to the questions,

The average of 17 numbers = 55

Sum of 17 numbers = 55 × 17

⇒ 935

The average of the first 6 numbers = 49.5

Sum of first 6 numbers = 49.5 × 6

⇒ 297

The average of the next 8 numbers = 60.5

Sum of next 8 numbers = 60.5 × 8

⇒ 484

Hence, the sum of 15th, 16th and 17th number = 935 - 297 - 484

⇒ 154

Let the 16th number be x, then

16th number = 15th number - 4

⇒ 15th number = x + 4

16th number = 17th number - 6

⇒ 17th number = x + 6

Hence, 15th number + 16th number + 17th number = 154

⇒ (x + 4) + x + (x + 6) = 154

⇒ 3x = 154 - 10

⇒ x = 48

The average of the 15th and 17th number

⇒ (x + 4 + x + 6)/2

⇒ (48 + 4 + 48 + 6)/2

⇒ 106/2 = 53

∴ The average of the 15th and 17th numbers is 53.

Given:

Length of 1st train = 120 m

Speed of 1st train = 34 km/h

Length of 2nd train = 180 m

Speed of 2nd train = 32 km/h

Concept Used:

1. When two trains travel in the opposite direction Relative Speed = S₁ + S₂
2. 1 km/hr = (5/18) m/s

Formula Used:

Time = (L₁ + L₂)/(S₁ + S₂)

Where, S₁ = Speed of 1st train, S₂ = Speed of 2nd train

L₁ = Length of 1st train, L₂ = Length of 2nd train

Calculation:

Time = = 300 × = 180/11 sec

∴ The total time taken by trains to cross each other is 180/11 sec.

Given:

The number of students in State A = 1.50 lakh

The number of students in State B = 1.40 lakh

The number of students in State C = 1.75 lakh

The ratio of passing: failing in state A = 6 : 5

The ratio of passing: failing in state B = 3 : 4

The ratio of passing: failing in state C = 8 : 2

Concept:

Ratio and proportion

Ratio - It is an ordered pair of numbers a and b, written a/b where b does not equal to 0.

Proportion - It is an equation where two ratios are set equal to each other.

Calculation:

Number of student passed in state B

=× 1.40 lakh

=×140000

= 60,000

= 0.6 lakh

Hence the correct answer is 0.6 lakh.

Given:

Vishnu left place A at 10 am. for place B.

Sudeep left place B at 2 pm. for place A.

The distance between the two places is 556 km.

Vishnu's speed is 42 km/h and Sudeep's speed is 55 km/h.

Formula used:

Distance = speed × time

Concept used:

If one object is moving with x km\h and another object is moving with y km/h in opposite direction,

Then their relative speed will be = (x + y) km / h

Calculation:

According to the question,

Vishnu went for (2 pm - 10 am) = 4 hr

In this 4 hr, Vishnu traveled = 42 × 4

⇒ 168 km

Remaining distance = 556 - 168

⇒ 388 km

The relative speed of Vishnu and Sudeep = 42 + 55

⇒ 97 km/h

Now relative distance = 388 km

Time taken = (388 /97)

⇒ 4hr

So, they will meet after 4hr from 2 pm.

∴ They will meet at 6 pm.

Additional Information

If one object is moving with x km\h and another object is moving with y km/h in same direction,

Then their relative speed will be = (x - y) km / h [ here, x > Y]

Given:

The present ages of Arun and Suresh are 24 years and 36 years respectively.

Calculation:

Arun age is 24 years and Suresh age is 36 years

8 years ago

Arun age = 24 - 8 = 16 years

Suresh age = 36 - 8 = 28 years

The ratio between the ages of Suresh and Arun, 8 years ago

⇒ 28 : 16

⇒ 7 : 4

∴ The ratio between the ages of Suresh and Arun, 8 years ago is 7 : 4.

Given:

C.P. for 1 T.V. = 24000

S.P. for 8 tv = 2,26,560

Concept used:

Profit/loss % = or

Calculation:

According to the questions,

C.P. for 8 T.V.= 8 × 24000 = 192000

Profit = 2,26,560 - 192000 = 34560

Profit % = × 100 % = 18 %

∴ The profit percentage is 18%.

Given:

Rate of interest = 12% per annum.

Time = 2 years.

Compound interest = Rs. 10176.

Concept:

Compound Interest Formula for 2 years:

CI = P(1 + R/100)^t - P

Using the compound interest formula for 2 years:

CI = P(1 + 12/100)² - P

10176 = P(1.12)² - P

⇒ 10176 = 1.2544P - P

⇒ 10176 = 0.2544P

⇒ P = 10176/0.2544

⇒ P = 40000

Therefore, the sum Priya borrowed was Rs. 40,000.

18 boys can do a piece of work in 24 days

1 boy can do a piece of work in (24 × 18) days

27 boys can do a piece of work = (24 × 18)/27 = 16 days

Given:

Ratio of x and y = 7 : 9

Calculation:

Let the x be 7 units and y be 9 units

Now,

3x - 5y : 4x + y

⇒ 3x - 5y = 3 × 7 - 5 × 9 = - 24

⇒ 4x + y = 4 × 7 + 9 = 37

∴ 3x - 5y : 4x + y = - 24/37

Let the speed of boat be ‘a’ and speed of stream be ‘b’.

Relative speed of boat going upstream = a – b

Relative speed of boat going downstream = a + b

Given, boat goes downstream in two-third the time it takes to go upstream.

Time = distance/speed

Distance is same in both cases.

⇒ 3a – 3b = 2a + 2b

⇒ a = 5b

Amount of tin in alloy A = (3/5) × 100 kg = 60 kg

Amount of tin in alloy B = (4/5) × 140 kg = 112 kg

Given:

R = 7 cm

Speed = 220 revs/min

Time = 20 minute

Concept:

Distance covered by a wheel in one revolution is equal to the circumference of the wheel.

Formula used:

Circumference of circle = 2πr

Speed = distance/time

Calculation:

Circumference = 2 × 22/7 × 7 = 44 cm

Distance = (44 × 220 × 20)/100

⇒ 1936 m

∴ The distance is 1936 m

Given:

The sales of an automobile company increased by 20% in 2020 as compared to the year 2019.

However in 2021, it fell by 20% as compared to the previous year.

It sold 6000 units in the year 2019

Calculations:

According to the question,

Sale increased by 20% in 2020 compared to 2019 = sale in 2019 (1 + 20%)

⇒ Sale in 2020 = 6000(1 + 20%)

⇒ Sale in 2020 = 6000(1 + 0.20)

⇒ Sale in 2020 = 6000(1.20) = 7200 units

Now sale decreased by 20% in 2021 compared to 2020 = sale in 2020(1 - 20%)

⇒ Sale in 2021 = 7200(1 - 20%)

⇒ Sale in 2021 = 7200(1 - 0.20)

⇒ Sale in 2021 = 7200(0.80) = 5760 units

∴ The company sold 5760 units in 2021.

Calculation:

⇒

⇒

⇒ 6x - 9y + 3 = 2x + 8y + 16

⇒ 4x - 17y = 13 ------(1)

⇒

⇒ 10x - 15y + 5 = 8x - 14y + 4

⇒ (2x - y = -1) × 2

⇒ 4x - 2y = -2 -------(2)

Subtracting equation (1) & (2), we get

⇒ 15y = -15

⇒ y = -1

By putting the value of y in equation (2), we get

⇒ x = -1

⇒ x + y = -1 + (-1) = -2

∴ The correct answer is -2.

Given:

a3 + 3a2 + 9a = 81

Calculation:

a3 + 3a2 + 9a = 81

⇒ a³ - 3a² + 6a² - 18a + 27a - 81 = 0

⇒ a²(a - 3) + 6a(a - 3) + 27(a - 3) = 0

⇒ (a - 3)(a² + 6a + 27) = 0

Considering (a - 3) = 0 only, since (a2 + 6a + 27) will yield complex roots,

(a - 3) = 0

⇒ a = 3

Now, a3 +

⇒ 3³ + 3/3

⇒ 27 + 1 = 28

∴ The required value is 28.

Given:
Cost Price of 30 mangoes = 1 rupee
Formula used:
Loss% = × 100
Calculation:
Cost Price of one mango = 1/30
Selling Price of x mangoes at loss 25% = 1 rupee
Selling Price of one mango at loss 25% = 1/x

1/120 = x-30/30x
x/4 = x - 30
x = 4x - 120
3x = 120
x = 40
Number of mangoes sold at 25% loss for one rupee is 40
Answer is 40.
Alternate Method
Given:
Cost Price of 30 mangoes = 1 rupee
Calculation:
Cost Price of one mango = 1/30
Let Cost Price be 100x
Loss 25% then,
Selling Price is 75x
100x = 1/30
x = 1/3000
75x = 75 × 1/3000
Selling Price of one mango = 1/40
Mangoes sold for a rupee at 25% loss is 40
Answer is 40.

Given:

Radius of sphere = 10 cm

Calculation:

In △OAB,

⇒ OA² + AB² = OB²

OB is the radius

⇒ AB² = 10² - 8²

⇒ AB² = 36

⇒ AB = 6 cm

∴ The radius of the curve of intersection of the plane and the sphere is 6 cm.

Calculation:

Total no. of employees in accounts department = 480

Male employees in the accounts department

⇒ 55% × 480 = 264.

Again,

Total no. of employees in marketing department = 360

Male employees in the marketing department

⇒ 40% × 360 = 144.

Total no. of male employees together in both department = 264 + 144 = 408

∴ The total number of male employees in the accounts and marketing department together is 408.

Given:

S = 15 days

S + R = 10 days = Rs. 1500

Formula used:

Efficiency = 1/time.

(1/15) + (1/R) = 1/10

10R + 150 = 15R

5R = 150

R = 150/5 = 30

Ramesh takes 30 days to do the same work alone.

The efficiency of Ramesh for 1 day = 1/30

The efficiency of Suresh for 1 day = 1/15

Hence, Money distribution:

For Ramesh: 1/30 x 1500 x 10= 500

For Suresh: 1/15 x 1500 x 10 = 1000

∴ the money divided between both of them is Rs. 1000, 500.

Given:

A, B and C start a business with their capitals in the ratio ∶ ∶

Calculation:

LCM of 5, 4 and 8 = 40

So, 40 × = 16, 40 × = 30, 40 × = 25

Let the investments of A, B, and C be 16x, 30x and 25x

Capital of A at the end of the year = 16x × 3 + (16x + 16x × 25%) × 9 = 228x

Capital of B at the end of the year = 30x × 3 + (30x - 30x × 20%) × 9 = 306x

Capital of C at the end of the year = 25x × 12 = 300x

Ratio of share of profit = 228x : 306x : 300x

⇒ 38 : 51 : 50

Now,

Share of C = 108420 × (50/139)

⇒ 39000

∴ The share (in Rs.) of C in the total profit of Rs. 108420 after one year is 39000.

Given:

Calculations:

Total number of visitors in Museum 1 = 220 + 230 = 450

Total number of visitors in Museum 2 = 370 + 195 = 565

Total number of visitors in Museum 3 = 57 + 380 = 437

Total number of visitors in Museum 4 = 245 + 219 = 464

∴ Maximum number of visitors are 565 i.e. in the Museum 2.

Concept used:

To convert to minutes to hours, divide the minutes by 60.

Formula used:

Distance = speed × time

Calculation:

Let speed of car be x km/h and the time taken to cover distance be y hour

Distance = xy ----(1)

According to the question:

If Shivani had travelled 6 km/h faster, and time taken 30 minutes less then,

Time = 30/60 = 1/2 hr

Speed = (x + 6)km/h

Time = (y – 1/2) hours

Distance = (x + 6)(y – 1/2)

From equation (1):

⇒ xy = (xy – x/2 + 6y – 6/2)

⇒ (xy – xy) = (- x/2 + 6y – 3)

⇒ -x + 12y – 6 = 0

⇒ - (x – 12y + 6) = 0

⇒ (x – 12y) = -6 ----(2)

Again,

If Shivani had travelled 5 km/h slower, and time taken 30 minutes more then

Time = 30/60 = 1/2 hr

Speed = (x – 5)km/h

Time = (y + 1/2) hours

Distance = (x – 5)(y + 1/2)

From equation (1):

⇒ xy = (xy + x/2 – 5y – 5/2)

⇒ (xy – xy) = (x/2 – 5y – 5/2)

⇒ x – 10y – 5 = 0

⇒ (x – 10y) = 5 ----(3)

Subtract from equation (2) to equation (3):

(x – 12y) – (x – 10y) = -6 – 5

⇒ x – 12y – x + 10y = -11

⇒ - 2y = - 11

⇒ y = 11/2

Now, put the value of y in equation (2);

(x – 12y) = -6

⇒ (x – 12 × 11/2) = -6

⇒ (x – 66) = -6

⇒ x = -6 + 66 = 60

Now, Distance = Speed × Time

Distance = 60 × 11/2 = 330 km

∴ The distance is 330 km.

Shortcut Trick

Distance = [{(S1 × S2)/(S1 − S2)} × t]

Where, S1 = First Speed

S2 = Second Speed

Calculation:

From both conditions,

S(S + 6)/6 × 30 = S(S − 5)/5 × 30

⇒ S(S + 6) × 5 = S(S − 5) × 6

⇒ 5S + 30 = 6S − 30

⇒ S = 60 km/hr

From the first condition:

Distance = [{S(S + 6)/6} × 30/60]

⇒ Distance = [{60(60 + 6)/6} × 30/60]

⇒ Distance = (60 × 66 × 30)/(6 × 60) = 330 km

∴ The distance is 330 km.

Given:

A bus travels at an average of 40 miles per hour for 2 hours.

And then travels at a speed of 60 miles per hour for 3 hours.

Formula used:

Speed = distance/time

Calculations:

Time in total = 3 + 2 = 5 hours(given)

Distance by bus = 40 × 2 miles = 80 miles

Distance by later = 60 × 3 miles = 180 miles

Total distance = 80 miles + 180 miles = 260 miles.

So, the bus travel in entire 5 hours = 260 miles.

∴ The answer is 260 miles.

Given:

SP of 72 shirts = CP of 80 shirts

Formula used:

P = S.P. – C.P.

L = C.P. – S.P.

P% = (P/C.P.) × 100

L% = (L/C.P.) × 100

Where,

P → Profit

L → Loss

SP → Selling price

CP → Cost price

Calculations:

Let the CP of 1 shirt be Rs.y and its SP be Rs.x.

So the SP of 72 shirts = 72x

And the CP of 80 shirts = 80y

According to the question,

72x = 80y

⇒ x ∶ y = 10 ∶ 9

Now let x and y be 10k and 9k respectively.

Since x > y

So P = 10k – 9k = k

P% = (P/CP) × 100

⇒ P% = (k/9k) × 100 = (100/9)%

∴ The required Profit% is (100/9)%.

Let the principle amount be P.
Simple interest for 3 years at 8% = (3 × 8 × P)/100 = .24P
Compound interest at 5% for 6 years = P × (1 + 0.05)⁶ – P  0.34P
The difference in two interests = 0.34P – 0.24 P = 0.1P
⇒ 0.1P = 5000
 ⇒ P = 50000
∴ The man borrowed Rs. 50000.