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Question 51

RBI Assistant 2023• Numerical Ability

A merchant marked the price of an article by increasing its production cost by 80%. Now he allows discount of Rs. 160 and gets a profit of Rs. 200 after selling it. The production cost is

  1. AOption (a)

    Rs. 320

  2. BOption (b)

    Rs. 360

  3. COption (c)

    Rs. 575

  4. DOption (d)

    Rs. 450

  5. EOption (e)

    Rs. 580

View answer & explanation

Correct answer

Answer: (d)D.

Rs. 450

Why this answer is correct

Solution:

Let the CP of the article is Rs. 100x

MP = 180/100 × 100x = 180x

Discount = Rs. 160

SP = MP - Discount

= 180x - 160          .............(i)

Also SP = CP + Profit

= 100x + 200        ...........(ii)

By equation (i) and (ii)

180x - 160 = 100x + 200

80x = 360

x = 36/8

CP of the article = 100x

= 100 × 36/8 = Rs. 450

Hence, option(4) is correct.

Question 52

RBI Assistant 2023• Numerical Ability

A train travelling at the speed of 144 km/h crossed a platform 100 m long in 30 seconds. Find the length of the train.

  1. AOption (a)

    1.3 km

  2. BOption (b)

    1.4 km

  3. COption (c)

    1.1 km

  4. DOption (d)

    1.2 km

  5. EOption (e)

    1.0 km

View answer & explanation

Correct answer

Answer: (c)C.

1.1 km

Why this answer is correct

Let the length of the train be x m.

Time taken by the train to cross 100 m platform = (x + 0.1)/144 h = 30/(60 × 60) h (given)

⇒ x + 0.1 = 144 × 0.5/60 = 1.2

⇒ x = 1.1

∴ The length of train is 1.1 km

Question 53

RBI Assistant 2023• Numerical Ability

Kamal decided to invest his amount in a ratio of 3 ∶ 2 in two schemes A and B at a rate of simple interest of 4% and 8% for 4 years and 2 years respectively. If he gets Rs. 12,00 as SI from both the scheme together, find the amount he invested.

  1. AOption (a)

    Rs. 6000

  2. BOption (b)

    Rs. 6500

  3. COption (c)

    Rs. 7500

  4. DOption (d)

    Rs. 8500

  5. EOption (e)

    Rs. 7000

View answer & explanation

Correct answer

Answer: (c)C.

Rs. 7500

Why this answer is correct

Given:

The ratio of the division of sum = 3 ∶ 2

Rate of interest on two schemes A and B respectively = 4% and 8%

Time for which it was invested in A and B respectively= 4, 2 years

Sum of SI = Rs. 1200

Formula used:

SI = PNR/100

P – Principal, N – Number of terms, R – Rate of interest

Calculation:

As the ratio of the sum is 3 ∶ 2, The amount will be 3x and 2x.

The amount obtained on scheme A = 3x × 4 × 4/100

The amount obtained on scheme A = 48x/100

The amount obtained on scheme B = 2x × 8 × 2/100

The amount obtained on scheme B = 32x/100

Sum of SI = 1200

⇒ 48x/100 + 32x/100 = 12,00

⇒ 80x/100 = 1200

⇒ x = 1500

Total amount he invested = 5x = 5 × 1500 = Rs. 7500

∴ The amount invested is Rs. 7500.

Question 54

RBI Assistant 2023• Numerical Ability

The present age ratio of person A to person B is 4:5. Two years from now, the age of person A will be 1(2/11) times the age that person B was eight years ago. What is the present age of person A?

  1. AOption (a)

    25 years

  2. BOption (b)

    35 years

  3. COption (c)

    30 years

  4. DOption (d)

    24 years

  5. EOption (e)

    20 years

View answer & explanation

Correct answer

Answer: (d)D.

24 years

Why this answer is correct

Solution:

Let's denote: A to be the present age of person A. B to be the present age of person B.

From the problem, we know that:

A/B = 4/5, which means A = (4/5) × B

A + 2 = 13/11 × (B - 8)

We can start solving this problem by substituting A from our first equation into the second equation:

(4/5) × B + 2 = 13/11 × (B - 8)

Multiplying all terms by 55 (to clear out the fractions), we get:

44B + 110 = 65B - 520

Solving for B, we get:

21B = 630

Which gives us B = 30.

Substituting B back into the first equation:

A = (4/5) × 30 = 24.

So, person A is 24 years old.

Question 55

RBI Assistant 2023• Numerical Ability

In the following question, two equations numbers I and II are given. you have to solve both equations and give the answer. 

 (I)  x2 - 6x + 9 = 0

 (II)  y2 + 8y +16 = 0

  1. AOption (a)

    x ≥ y

  2. BOption (b)

    x ≤ y

  3. COption (c)

    x > y

  4. DOption (d)

    x < y

  5. EOption (e)

    x = y or relation can not be established 

View answer & explanation

Correct answer

Answer: (c)C.

x > y

Why this answer is correct

Calculations:

(I) x2 - 6x + 9 = 0

 ⇒  x2 - 3x - 3x + 9 = 0

 ⇒ x(x - 3) -3(x - 3) = 0

 ⇒ (x - 3) (x - 3) = 0

 ⇒   x = 3, 3

(II)  y2 + 8y + 16 = 0

 ⇒   y2 + 4y + 4y +16 = 0

 ⇒   y(y + 4) + 4(y + 4) = 0

 ⇒   (y + 4) (y + 4) = 0 

 ⇒     y = - 4 , - 4 

Value of  xValue of yRelation
3- 4x > y
3- 4x > y
3- 4x > y
3- 4x > y

Hence x > y.

Question 56

RBI Assistant 2023• Numerical Ability

In the given question, two equations numbered l and II are given. Solve both equations and mark the appropriate answer.

I.  y2 – 6y – 112 = 0

II. x2 + 3x – 40 = 0

  1. AOption (a)

    x ≤ y

  2. BOption (b)

    x > y

  3. COption (c)

    x ≥ y

  4. DOption (d)

    x < y

  5. EOption (e)

    x = y or relation between x and y can not be established

View answer & explanation

Correct answer

Answer: (e)E.

x = y or relation between x and y can not be established

Why this answer is correct

Solutions:

For I:

y2 – 6y – 112 = 0

⇒ y2 – 14y + 8y – 112 = 0

⇒ y(y – 14) + 8(y – 14) = 0

⇒ (y – 14) (y + 8) = 0

⇒ y = 14, -8

For II:

 x2 + 3x – 40 = 0

⇒ x2 + 8x – 5x – 40 = 0

⇒ x(x + 8) – 5(x + 8) = 0

⇒ (x + 8) (x – 5) = 0

⇒ x = -8, 5

Comparison between x and y (via Tabulation):

Value of yValue of xRelation
14-8x < y
145x < y
-8-8x = y
-85x > y

So x = y or relation between x and y can not be established.

Question 57

RBI Assistant 2023• Numerical Ability

In the given question, two equations numbered l and II are given. Solve both equations and mark the appropriate answer.

I.  x2 – 2x – 48 = 0

II. y2 – 4y – 252 = 0

  1. AOption (a)

    x = y or relation between x and y can not be established

  2. BOption (b)

    x ≥ y

  3. COption (c)

    x < y

  4. DOption (d)

    x ≤ y

  5. EOption (e)

    x > y

View answer & explanation

Correct answer

Answer: (a)A.

x = y or relation between x and y can not be established

Why this answer is correct

Solutions:

For I:

x2 – 2x – 48 = 0

⇒ x2 – 8x + 6x – 48 = 0

⇒ x(x – 8) + 6(x – 8) = 0

⇒ (x + 6) (x – 8) = 0

⇒ x = -6, 8

For II:

y2 – 4y – 252 = 0

⇒ y2 – 18y + 14y – 252 = 0

⇒ y(y – 18) + 14(y – 18) = 0

⇒ (y – 18) (y + 14) = 0

⇒ y = 18, -14

Comparison between x and y (via Tabulation):

Value of xValue of yRelation
-618x < y
-6-14x > y
818x < y
8-14x > y

So x = y or relation between x and y can not be established.

Question 58

RBI Assistant 2023• Numerical Ability

In the following question, two equations numbers I and II are given. you have to solve both equations and give the answer. 

 (I)  2x2  + 9x - 45 = 0

 (II)  2y2 + 5y - 52 = 0

  1. AOption (a)

    x > y

  2. BOption (b)

    x < y

  3. COption (c)

    x ≥ y

  4. DOption (d)

    x ≤ y

  5. EOption (e)

    If x = y  or no relation can be established

View answer & explanation

Correct answer

Answer: (e)E.

If x = y  or no relation can be established

Why this answer is correct

Calculation:

From I equation

(I) 2x2  + 9x - 45 = 0

⇒ 2x2 + 15x - 6x - 45  = 0 

⇒ x(2x + 15) - 3(2x + 15) = 0

⇒ (2x +15) (x - 3) = 0 

⇒ x = - (15/2) = - 7.5 or x = 3

⇒ x = -7.5 or 3.

(II) 2y2 + 5y - 52 = 0

⇒ 2y2 + 13y - 8y - 52 = 0

⇒ y(2y + 13) - 4(2y + 13) = 0

⇒ (2y + 13) (y - 4) = 0

⇒ y = - (13/2) = - 6.5 or y = 4.

⇒ y = -6.5 or 4.

Value of xValue of yRelation between x and y
- 7.5- 6.5x < y
- 7.54x < y
3- 6.5x > y
34x < y

Hence, there is no relation can be established between them.

Question 59

RBI Assistant 2023• Numerical Ability

Two equations I and II are given below in the question. You have to solve these equations and give the answer.

I. 9x2 – 15x + 4 = 0

II. 7y2 + 18y + 8 = 0

  1. AOption (a)

    x < y

  2. BOption (b)

    x > y

  3. COption (c)

    x ≤ y

  4. DOption (d)

    x ≥ y

  5. EOption (e)

    x = y or the relation between x and y can't be established.

View answer & explanation

Correct answer

Answer: (b)B.

x > y

Why this answer is correct

Shortcut Trick 

I. 9x2 – 15x + 4 = 0

There are three terms = a, b, and c

Where 'a' = value of x2, 'b' = Value of x, 'c' = 4

If value of 'c' is positive value and value of 'b' is negative value, then both the values of x is POSITIVE value.

II. 7y2 + 18y + 8 = 0

There are also three terms = a, b, and c

Where 'a' = value of y2, 'b' = Value of y, 'c' = 8

If the value of 'c' is a positive value and the value of 'b' is also a positive value, then both value of y is NEGATIVE value.

∴ After comparison, all the values of x and y, the relation between x and y is "x > y".

Given:

I. 9x2 – 15x + 4 = 0

II. 7y2 + 18y + 8 = 0

Calculation:

I. 9x2 – 15x + 4 = 0

⇒ 9x2 – 12x – 3x + 4 = 0

⇒ 3x(3x – 4) – 1(3x – 4)= 0

⇒ (3x – 4)(3x – 1) = 0

⇒ x = 4/3, 1/3

II. 7y2 + 18y + 8 = 0

⇒ 7y2 + 14y + 4y + 8 = 0

⇒ 7y(y + 2) + 4(y + 2) =0

⇒ (y + 2)(7y + 4) = 0

⇒ y = (-2), (-4/7)

Value of ‘x’RelationValue of ‘y’
4/3>-2
4/3>-4/7
1/3>-2
1/3>-4/7

 

When we compared the values of ‘x’ and ‘y’ in the table above, we found that there is only ONE relation between X and Y i.e. >. So, a relation between x and y is “x > y”.

∴ After comparison, all the values of x and y the relation is “x > y”.

Question 60

RBI Assistant 2023• Numerical Ability

The sum of the perimeter of the rectangle and circle is 138 cm. The ratio between the length of the rectangle and the radius of the circle is 10: 7. If the breadth of the rectangle is 5/14 times the radius of the circle. Then, find the area of the rectangle (in sq. cm)?

  1. AOption (a)

    64

  2. BOption (b)

    100

  3. COption (c)

    120

  4. DOption (d)

    140

  5. EOption (e)

    125

View answer & explanation

Correct answer

Answer: (b)B.

100

Why this answer is correct

Given:

Sum of the perimeter of rectangle and circle = 138 cm

The ratio between the length of rectangle and radius of circle = 10: 7

The breadth of Rectangle = 5/14 × Radius of Circle

Formula Used:

Perimeter of rectangle = 2(length + breadth)

The perimeter of circle = 2πr

Area of rectangle = (length × breadth)

Calculation:

Suppose the length of the rectangle and the radius of the circle is 10x and 7x, respectively.

Breadth of the rectangle = 5/14 × (7x) = 5x/2

According to question –

Sum of the perimeter of rectangle and circle = 138 cm

⇒ 2(10x + 5x/2) + 2π(7x) = 138

⇒ 25x + 44x = 138

⇒ 69x = 138

⇒ x = 138/69

⇒ x = 2

Length of rectangle = 10x = 20 cm

Breadth of rectangle = 5x/2 = 5 cm

∴ Area of the rectangle = length × breadth

⇒ (20 × 5)

⇒ 100 cm2

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