Maths & Logical Reasoning Test - 9 - SSC CGL MCQ

Given:

Mr. Shiva invested equal amount of money in two private firms

And for different times 3.5 and 5 years

And the difference between in their interests = 225

Formula used:

S.I = (P × R × T)/100

Calculation:

Let the amount of money invested by Shiva is Rs. x

So, the simple interest on the principal x for 3.5 years = (x × 15 × 3.5)/100

And the simple interest on the principal x for 5 years = (x × 15 × 5)/100

According to question,

Difference between the interests = 225

So, (x × 15 × 5)/100 - (x × 15 × 3.5)/100 = 225

⇒ (5 – 3.5) 15x/100 = 225

⇒ x = (225 × 100)/(15 × 1.5)

⇒ x = 1000

The amount of money invested by Shiva is Rs. 1000 × 2 = Rs.2000

∴ The amount invested by Mr. Shiva is Rs. 2000.

Let the total profit at the end of 11 months = Rs. X

Since A receives Rs. 1050 per month salary out of the profit

⇒ Total salary taken by A, out of profit = 1050 × 11 = Rs. 11550

⇒ Amount of donation done out of the profit = 12.5% of X = Rs. X/8

⇒ Remaining profit to be shared between all three in the ratio of their investment is

X – 11550 – X/8 = (7X/8 – 11550)

Ratio in which remaining profit will be shared = 9 : 7 : 5

Since A receives Rs. 450 less than B and C together

⇒

⇒ (X/8) - 1650 = 12000

⇒ (X/8) = 13650 

⇒ X = 109200

∴ Total profit at the end of 11 months = Rs. 109200

Concept use:

Sum of all values = Mean × Number of values

Explanation:

Let's find the sum of the given data values, excluding x:

12 + 15 + 18 + 21 + 27 + 30 + 33 + 36 = 192

We know that the mean is the sum of all values divided by the total number of values.

Given:

Mean = 24

Number of values = 9 (including x)

Sum of all values = Mean × Number of values

Sum of all values = 24 × 9 = 216

Since the sum of the given values (excluding x) is 192, we can find x by subtracting 192 from 216.

x = 216 - 192 = 24
Hence, The Correct Answer is Option 2.

Solution:

Let Maria's only son's present age be x years and her daughter's present age be y years.

and Let Maria's present age be z years and her husband's present age be w years.

Eight years ago,

Maria's age = z - 8 = x + y . . .(i)

10 years from now,

son's age = x + 10 and daughter's age = y + 10

ATQ: (y + 10)/(x + 10) = 6/5

⇒ 5y + 50 = 6x + 60

⇒ 5y - 6x = 10 . . .(ii)

Since, Maria's husband is 8 years older than her.

⇒ w = z + 8 . . .(iii)

Husband's present age is four times that of her son

⇒ w = 4x . . .(iv)

From (iii) and (iv),

z = 4x - 8 . . .(v)

From (v) and (i),

4x - 8 - 8 = x + y

⇒ 3x - y = 16 . . .(vi)

⇒ 2 × (vi) + (ii), we get

⇒ 5y - 2y = 10 + 32 ⇒ 3y = 42

⇒ y = 14

Hence, present age of Maria's daughter is 14 years.

Given:

The thief started cycling at 7:30 pm
The policeman started half an hour later at 8:00 pm
The thief's speed is 10 km/h.
The policeman's speed is 12 km/h.

Formula used:

Distance = Speed × Time

Calculation:

Let t be the time it takes for the policeman to catch the thief.

In the half-hour interval between the thief's departure and the policeman's departure

The thief travels, Distance = Speed × Time

D = 10 × (1/2) km = 5km

So, when the policeman starts at 8:00 P.M., the thief is already 5 km away

Now,

Distance covered by the policeman = Relative speed × t

⇒ Relative speed = (12 - 10) = 2 km/h

Now,

⇒ 2km/h × t = 5 km

⇒ t = (5/2) = 2.5 hours 
Since the policeman started at 8:00 P.M., he will catch the thief 2.5 hours later:

8:00 pm + 2:30 hours = 10:30 pm

∴ The policeman will catch the thief at 10:30 pm

GIVEN:

A's principle = 8,000

Rate = 8% at S.I.

B's principle = 6,000

Rate = 10%at C.I.

FORMULA USED:

S.I. = ( P × R × T )/100

A = P × (1 + (R/100))^t

C.I. = Amount - Principle

Where, A = Amount , S.I. = Simple Interest, C.I.= Compound Interest

P = Principle, R = Rate , t = time in years

CALCULATION:

As, we have, A's Principle = Rs8,000 , Rate = 8% , Time = 3 years

⇒ S.I. = ( P × R × T)/100 = ( 8000 × 8 × 3)/100 = Rs1,920.

Now, we have B's Principle = Rs6,000, Rate = 10% , Time = 3 years

⇒ A = P × (1 + (R/100)^t) 

⇒ A = 6000 × ((1 + (10/100)³)  = 6000 × 11/10 × 11/10 × 11/10 = Rs7,986.

Now, the Compound Interest = (Amount - Principle) = (7986 - 6000) = Rs1,986

After 3 years, Difference = (1,986 - 1,920) = Rs66.

Hence, the required difference after 3 years is Rs 66.

Concept use:

The Sum of Angles of Quadrilateral = 360°

Calculation:

The angles of the quadrilateral are in the ratio 4 : 5 : 10 : 11.

∴ 4x + 5x + 10x + 11x = 360°

⇒ 30x = 360° ⇒ x = 12°

Hence, The Angles of Quadrilaterals are 48°, 60°, 120°, 132°

Hence, The Correct Answer is 48°, 60°, 120°, 132°.

Given:

Sachin lent Rs. 20000 to Ankit at simple interest at the rate of 10% per annum for 2 years.

Ankit lent half of the money to Gaurav at simple interest at the rate of 5% per annum for 2 years.

And lent rest half of the money to Amar at compound interest at the rate of 10% per annum.

Formula used:

S.I = P × R × T/100

C.I = P [(1 + R/100) ⁿ – 1], n = number of years

Calculation:

Simple interest paid by Ankit to Sachin = Rs. 20000 × 10 × 2/100 = Rs. 4000

Simple interest paid by Gaurav to Ankit = Rs. 10000 × 5 × 2/100 = Rs. 1000

Compound interest paid by Amar to Ankit = 10000 [(1+ 10/100)² – 1] = Rs. 2100

So, total amount received by Ankit = 1000 + 2100 = Rs. 3100

Given:

There is a provision for 15 days of food for 60 boys

After 5 days, 15 more boys joined the hostel

Concept Used:

Total Food = No. of Days × No. of Boys

Calculation:

Total Food = 15 × 60 = 900 units

According to the question

Total Food for 5 days = 5 × 60 = 300 units

Remaining Food = 900 - 300 = 600 units

New number of boys = 60 + 15 = 75

So the remaining food will last for (600 ÷ 75) = 8 days

∴ After 5 days if 15 more boys are joined, food will last for 8 more days.

Given:

First number = 2

Second number = 4

Formula Used:

LCM of two numbers = (Product of the numbers) / GCD (Greatest Common Divisor) of the numbers

Calculation

First, find the GCD of 2 and 4.

⇒ GCD of 2 and 4 = 2

Then, use the formula to find the LCM.

⇒ LCM = (2 × 4) / 2

⇒ LCM = 8 / 2

⇒ LCM = 4

Hence, the LCM of 2 and 4 is 4.

In ∆CDE
∠ECD + ∠EDC = 180° – 52° = 128°
As CE and DE are angle bisectors of ∠C and ∠D
∠C + ∠D = 2 × 128° = 256°
∠B = 360° – 35° – 256° = 69°
Hence, option C is correct.

∠A + ∠B + ∠C + ∠D = 360
∠C + ∠D = 360° – (∠A + ∠B)
In ∆ COD


∠COD = 180° – ∠ODC – ∠OCD
= 180° – (∠ODC + ∠OCD)


Hence, option C is correct.

x = 3 and y = 2



= A² + AB + B²
= 9² + 9 × 20 + 20²
= 661
Hence, option A is correct.

CO = 10 cm
In ∆CPE,


R = 15 cm
Hence, option C is correct.

Using the relation AM > GM

Given, a + b = 40
∴ 20 > √ab
⇒ ab < 400
Thus, maximum value of ab = 400
Solving, a + b = 40 and ab = 400
We get a = b = 20
Thus, ab is maximum when a = b.
Hence, option (D) is correct.

5sin A + 2cosA = 3 ---- (1)
25sin²A + 4cos²A + 20 sin A cos A = 9 ---- (2)
5cosA – 2sinA = y
25cos²A + 4sin²A – 20sinAcosA = y² ---- (3)
Add eq (2) and (3)
29 = y² + 9
±2√5 = y = 5cosA – 2sinA ---- (4)
On solving (1) and (4)
29cosA = 6 ± 10√5
Hence, Option C is correct.

Given: (850, 645, 410)

The logic followed here is:

(850, 645, 410) → 850 - 645 = 205 → 205 × 2 = 410

By checking options,

(1) (751, 396, 544) → 751 - 396 = 355 → 355 × 2 = 710

(2) (558, 256, 356) → 558 - 256 = 302 → 302 × 2 = 604

(3) (440, 229, 422) → 440 - 229 = 211 → 211 × 2 = 422

(4) (550, 402, 135) → 550 - 402 = 148 → 148 × 2 = 296

Hence, (440, 229, 422) is the correct answer.

Hence, mirror image of the given figure will be option 1.

• The image obtained when the paper is unfolded is as shown below:

• Hence, the correct answer is "Option (3)".

The logic followed here is:

From figure B to A:

• All shapes shifted in an anticlockwise direction.
• Arrow Shifted in the center and it is rotating 90 degrees in a clockwise direction.

Similarly,

From figure D to C:

• All shapes shifted in an anticlockwise direction.
• Arrow Shifted in the center and it is rotating 90 degrees in a clockwise direction.

Hence, the correct answer is "Option 2".

Given: 2, 3, 6, 15, 45, ?

The logic follows here is:

Hence, the correct answer is "157.5".

So from the venn diagram, both conclusions, i.e., I and II follow.
Hence, the correct answer is option C.

Using the above information we get,

 
Now, since we do not have the exact position of O and Q. We cannot determine the required answer.
Hence, option D is correct.

On interchanging + and –, we get

161 + 99 ÷ 11 – 5 × (25 – 5) + 20 = 90

161 + 9 – 100 + 20 = 90

90 = 90

LHS = RHS
Hence, option C is correct.

(a) N – K + L ⇒  
Using option (A) we get N is the brother of K and K is the father of L
Here gender of L is not clear so L can either be Nephew or Niece of N.
(b) N + K – L ⇒
Using option (B) we get N is the father of K and K is the brother of L.
Here L is either son or daughter of N.
(c) N + K × L ⇒
Using option (C) we get N is the father of K and L is the daughter of K.
Here L is the granddaughter of N.
Hence, option D is correct.

Any media message which promotes social disintegration would be detrimental with the future business of the company and therefore it is of utmost importance to shun the advertisement and modify it.

Hence, Option C is the correct answer.

Except for option D, in rest all the difference between the numbers gives a perfect square number.
(324, 405) → 405 – 324 = 81 = 9²
(426, 490) → 490 – 426 = 64 = 8²
(633, 754) → 754 – 633 = 121 = 11²
(522, 581) → 581 – 522 = 59
Hence, Option D is correct.

Business are bound to be risky and therefore demotivation will not help in such scenario. Thereby, strategizing and taking calculated risk is the best possible way out.
Hence, option  D is correct.

Hence, option D is correct.

By close observation, we get the mirror image of  " R P 9 S 1 L" is "".
Hence, option D is correct.