RPF Constable Arithmetic Test – 01

Given :  

The ratio of alpha's age to beta's age is 2 : 5.

The sum of their ages is 252.

Calculation:

Let alpha's age be 2x.

Let beta's age be 5x.

The difference in their ages is 5x - 2x = 3x.

2x + 5x = 252 (sum of their ages).

7x = 252

x = 36

So, alpha's age is 2x = 72 and beta's age is 5x = 180.

Therefore, the difference in their ages is 5x - 2x = |72 - 180| = 108.

Hence, the difference in their ages is 108.

Calculation:

Total production by company X in the years from 2001 to 2006 = 37 + 41 + 49 + 62 + 27 + 34 = 250

Total production by company Y in the years from 2001 to 2006 = 63 + 58 + 68 + 67 + 57 + 62 = 375

Difference between the total production of the two companies in the years given by the X and Y companies in the years from 2001 to 2006 = 375 - 250

⇒ 125

Given:

Cost price (CP) of the item = Rs. 405
Selling price (SP) of the item = Rs. 324

Formula:

% Loss =  Loss/ CP ×  100

Loss = CP - SP

Calculation:

Loss = 405 - 324

⇒ Rs. 81

Loss% = Loss/ CP ×  100

⇒ 181/405 × 100

⇒ 20%

Given:

The sides of a quadrangular plain are in the ratio 2:3:4:5
The perimeter of the quadrangular plain is 574 cm

Formula:

If the sides of a quadrilateral are a, b, c, and d, then the perimeter of the quadrilateral is given by:

Perimeter = a + b + c + d

Calculation:

Using the given ratio of the sides of the quadrangular plain, we can assume that the sides are 2x, 3x, 4x, and 5x.

Therefore, we can write:

Perimeter = 2x + 3x + 4x + 5x

574 = 14x

x = 41

So, the sides of the quadrangular plain are:

2x = 2 × 41 = 82 cm

3x = 3 × 41 = 123 cm

4x = 4 × 41 = 164 cm

5x = 5 × 41 = 205 cm

The smallest arm is the smallest side of the quadrangular plain, which is 82 cm.

Calculation:

Number of vehicles manufactured by Company X in 2001 = 37

Number of vehicles manufactured by Company X in 2002 = 41

Difference between the number of vehicles manufactured in 2001 and 2002 by Company X = 41 - 37

⇒ 4

Calculation:

Let the number be x. Then we can translate the given information into the following equation:

0.25 ×  0.6667 × 0.75 × 0.8 × x = 6349

Simplifying the left-hand side, we get:

0.25 × 0.6667 × 0.75 × 0.8 × x = (1/4) × (1/3) × (3/4) × (4/5) × x = 0.1x

Substituting the given value of 0.1x in the equation, we get:

0.1x = 6349

Dividing both sides by 0.1, we get:

x = 63490

Therefore, the number is 63490.

To find 40% of this number, we can multiply it by 0.4:

40% of 63490 = 0.4 × 63490 = 25396

Therefore, 40% of the number is 25396.

Given:

Length of diagonal = 92 cm

Formula:

In a square, the length of the diagonal is √2 times the length of a side.

So, diagonal = √2 x side

Area of a square = side²

Solution:

Let the side of the square be 'a' cm.

According to the formula mentioned above:

92 = √2 x a

a = 92/√2

Therefore, the area of the square is:

Area = a²

Area = (92/√2)²

Area = 4232 cm²

Hence, the area of the square is 4232 cm².

Given:

Principal (P) = Rs. 4,800

Rate of interest (R) = 13%

Time (T) = 4 years

Formula:

Simple Interest (SI) = (P ×  R ×  T) / 100

Amount (A) = P + SI

Calculation:

SI = (4800 × 13 ×  4) / 100 = Rs. 2,496

A = P + SI = 4800 + 2496 = Rs. 7,296

Therefore, the amount to be received after 4 years at Rs. 4,800 for 13% per annum simple interest is Rs. 7,296.

Given:

LCM = 132

HCF = 11

One number = 11

Formula:

Product of two numbers = LCM × HCF

We can use this formula to find the second number.

Solution:

Let the second number be x.

The product of the two numbers is equal to the product of their LCM and HCF.

So, we have:

11 ×  x = 132 ×  11

x = (132 ×   11)/11

x = 132

Therefore, the second number is 132.

Solution:

To determine which of the given numbers are divisible by 15, we need to check if they are divisible by both 3 and 5.

If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. Therefore, we can check if the numbers are divisible by 3 by adding their digits.

To check if a number is divisible by 5, we only need to check if its last digit is 0 or 5.

Let's check each of the given numbers:

a) 73445: The sum of its digits is 7 + 3 + 4 + 4 + 5 = 23, which is not

divisible by 3, and its last digit is 5, which is divisible by 5. So, 73445

is not divisible by 15.

b) 38445: The sum of its digits is 3 + 8 + 4 + 4 + 5 = 24, which is

divisible by 3, and its last digit is 5, which is divisible by 5. So, 38445

is divisible by 15.

c) 39445: The sum of its digits is 3 + 9 + 4 + 4 + 5 = 25, which is not

divisible by 3, and its last digit is 5, which is divisible by 5. So, 39445 is not divisible by 15.

d) 64345: The sum of its digits is 6 + 4 + 3 + 4 + 5 = 22, which is not

divisible by 3, and its last digit is 5, which is divisible by 5. So, 64345

is not divisible by 15.

Therefore, only the number b) 38445 can be divided by 15.

Given:

The speed of the train is 51 m/s.

The time taken to cross a signal is 13 seconds.

Formula:

Let the length of the train be 'l' meters. Then, the distance covered by the train in crossing the signal is 'l' meters.

The speed of the train is given as 51 m/s. Therefore, the distance covered by the train in 1 second is 51 meters.

Using the formula, distance = speed x time, we can calculate the distance covered by the train in 13 seconds as 51 x 13 = 663 meters.

Since the distance covered by the train in crossing the signal is 'l' meters, we have:

l = distance covered by the train in 13 seconds

Solution:

Using the formula, we have:

l = distance covered by the train in 13 seconds

l = 51 x 13

l = 663

Therefore, the length of the train is 663 meters.

Calculation:

⇒ 12 - [24 - (72 ÷ 3 - (30 - 50 ÷ 5) ÷ 20)]

⇒ 12 - [24 - (72 ÷ 3 - (30 - 10) ÷ 20)]

⇒ 12 - [24 - (72 ÷ 3 - 20 ÷ 20)]

⇒ 12 - [24 - (24 - 1)]

⇒ 12 - [24 - 24 + 1]

⇒ 12 - 1

⇒ 11