SSC GD Practice Maths Question For 2023 Set-1

SSC GD Practice For Most Important Maths Question For 2023 Set-1–With Solution

1 .If the number 481A673 is completely divisible by 9, what is the smallest whole number in place of A?

• 15
• 7
• 6
• 16

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Solution

Concept:

Divisblity rule of 9: if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9

Calculation:

We have 481A673

If the number is divisible by 9 then

4 + 8 + 1  + 6 + 7 + 3 = multiple of 9

⇒ 29 + A = multiple of 9

If A = 7, sum become 36 which is divisible by 9.

∴ Smallest whole number is 7. 

2. Rupam borrows from a bank at 10% compound interest per annum. After how much time the compound interest will become 21% of the principal?

• 1 years
• 2 years
• 3 years
• 4 years

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Solution

Given:

Rupam borrows from a bank at 10% compound interest per annum.

Formula used:

A = P (1 + R/100)^T

Calculation:

Let Principal (P) = 100

∴ Amount (A) = 121

⇒ 121 = 100 × (1 + 10/100)^T

⇒ (1 + 10/100)T = 121/100

⇒ (11/10)T = (11/10)² 

T = 2 Years

∴  After 2 years, the compound interest will become 21% of the principal. 

3. If the compound interest earned for the 2nd year is Rs. 240 and the rate of interest applied is 20% per annum, then find the principal invested.

• Rs. 100043% answered correctly
• Rs. 2000
• Rs. 1200
• Rs. 2400

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Solution

Given:

The compound interest earned for the 2nd year = Rs. 240,

R = 20% p.a.

Formula used:

(1.) C.I_n+1 = (1 + R%) × C.I_n

Where,  

C.I_n = Compound interest earned for nth year

C.In+1 = Compound interest earned for (n + 1)th year

R = rate of interest applied

(2.) S.I = PRT100PRT100

Where, 

P = Principal 

R = Rate of interest applied

T = Time invested

Concept used:

Simple interest and Compound interest are the same for the first year.

Calculation:

According to the question,

⇒ C.I2 = (1 + 20%) × C.I1

⇒ Rs. 240 = (1 + 20%) × C.I1

⇒ Rs. 240 = 1.2 × C.I1

⇒ C.I1 = Rs. 200

Now, 

Let P be the principal invested.

Since simple interest and compound interest are the same for the first year,

Therefore, 

⇒ 200 = P×20×1100P×20×1100

⇒ P = Rs. 1000

Therefore, ‘Rs. 1000’ is the required answer.

4.If an observation 70 is removed from the data 60, 68, 70, 72, 74, 76, 78, 80, then the median is increased by:

• 0.5
• 1
• 1.5
• 2

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Solution

Given:

Observations are 60, 68, 70, 72, 74, 76, 78, 80

Concept used:

The following steps are helpful while applying the median formula for ungrouped data.

• Step 1: Arrange the data in ascending or descending order.
• Step 2: Secondly, count the total number of observations ‘n’.
• Step 3: Check if the number of observations ‘n’ is even or odd.

Median Formula When n is Odd

Median = [(n + 1)/2]^th term

Median Formula When n is Even

Median = [(n/2)^th term + ((n/2) + 1)^th term]/2

Calculation:

As the numbers are already in the increasing order so we don’t need to arrange them

Now, median = 4thterm+5thterm24thterm+5thterm2

⇒ 72+74272+742

⇒ 73

Now, if 70 is removed the new median will be = 4th term,

⇒ 74

So, median increased = 74 – 73

⇒ 1

∴ Required increased in the median is 1.

5.Simple interest on a certain sum is 16/25 of the sum. Find the rate per cent and time, if both are equal.

• 8% and 8 years
• 6% and 6 years
• 10% and 10 years
• 12% and 12 years

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Solution

Formula used:

SI = (P × R × T)/100

Calculation:

Let the rate and time be ‘r’ and the Principle be x

∴ According to the given conditions,

⇒ 16x/25 = (x × r × r)/100

∴ r × r = (16/25) × 100

∴ r = (4/5)× 10 = 8∴ The required rate and number of years are 8% and 8 years.

6. A person goes from A to B with speed 40 km/hr & return from B to A with speed 30 km/hr. Whole journey takes 14 hr, then find the distance between A & B in Km.

• 480
• 2404
• 120
• 360

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Solution

Given:

Speed = 40 kmph and 30 kmph (on return)

Total time = 14 hours

Formula:

Distance = Speed × Time

Calculation:

Let the distance be ‘D’ km

According to the question,

D/40 + D/30 = 14

⇒ (3D + 4D)/120 = 14

⇒ 7D/120 = 14

⇒ D = 240 km

∴ Distance between A & B = 240 km

7. Jeevan fills a wall in his room with the photos he took. The size of a photo is 21 cm by 18 cm. If he uses 6 photos, then what is the area of the wall?

• 2068 sq cm
• 2268 sq cm
• 378 sq cm
• 2334 sq cm

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Solution

Given:

The size of photo = 21 cm by 18 cm

Number of photos used = 6

Formula used:

Area of rectangle = l × b

Calculation:

The size of photo = 21 cm by 18 cm

Area of frame = 21 × 18 = 378 cm²

Number of photos used = 6

∴ Total area covered by photos = 378 × 6 = 2268 sq cm

8. If the area of a triangle is 1,815 cm² and the ratio of its base and the corresponding altitude in 5 : 6, then what is the altitude (in cm) of the triangle?

• 66
• 42
• 56
• 55

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Solution

Given:

Area of triangle = 1,815 cm².

the ratio of its base and the corresponding altitude in 5 : 6.

Formula used:

Area of triangle = (1/2) × base × altitude

Calculation:

Let the base and altitude be 5x and 6x.

(1/2) × 5x × 6x = 1815

⇒ 15x² = 1815

⇒ x² = 121

⇒ x = 11

Altitude = 6(11)

⇒ 66 cm

∴ Altitude is 66 cm.

9. A room’s length is double of its width and width is one third of its height. If the area four walls is 2592 m², what is the height of this room ?

• 36 m.
• 30 m.
• 34 m.
• 28 m.

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Solution

Given:

A room’s length is double of its width and width is one third of its height. If the area four walls is 2592 m2

Concept used:

Curved surface area of cuboid = 2h(l + b)

Calculation:

Let Height of room = x

Width of room = 1/3 of x = x/3

Length of room = 2x/3

Curved surface area of cuboid = 2h(l + b) = 2x (x/3 + 2x/3) = 2592

⇒ 2x² = 2592 m²

⇒ x = 36 m

∴ Height of room is 36 m

10. The body weight of seven boys is recorded as 70 kg, 64 kg, 55 kg, 81 kg, 45 kg, 76 kg and 92 kg. What is the average body weight of all seven boys?

• 69 kg
• 96 kg
• 65 kg
• 56 kg

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Solution

Given:

The body weight of seven boys is recorded as = 70 kg, 64 kg, 55 kg, 81 kg, 45 kg, 76 kg and 92 kg.

Formula used:

Average = Sum of the numbers/Total number.

Calculation:

Average = (70 + 64 + 55 + 81 + 45 + 76 + 92)/7 = 483/7 = 69 kg

Hence, the correct answer is “69 kg”.

11. Which is the greatest four digit number that is exactly divisible by 15, 32, and 48?

• 9980
• 9896
• 9600
• 9988

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Solution

Concept used:

in this type of questions

first we take the L.C.M. of the given numbers.

Calculation:

 Factor of the given numbers :

15 = 3 × 5

 32 = 2⁵

 48 = 2⁴ × 3  

L.C.M. of 15 , 32 and 48 = 2⁵ × 3 × 5 = 480

The largest 4 digit number is 9999.

When we divide the largest 4 digit number i.e. 9999 by 480 , we find the remainder 399 & when we substract this number from 9999 , we will get the largest 4 digit number which is exactly divisible by 15, 32, 48.

Therefore,

The number is : 9999 – 399 = 9600

Hence, the correct answer is “9600”.

12. An article was marked at 20% above its cost price and a discount of 20% is given on the marked price. Find the profit or loss percentage.

• Neither profit nor loss
• 4% Loss81% answered correctly
• 8% Profit
• 10% Profit

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Solution

Given:

An article was marked at 20% above its cost price

A discount of 20% is given on the marked price.

Formula used:

S.P = C.P [1 – Los%/100] 

S.P = selling price , C.P = cost price 

Calculation:

C.P = 100 

Market price = 100 + 20 = 120 

⇒ Discount = 20/100 × 120 = 24 

⇒ S.P = 120 – 24 = 96

⇒ Loss = 100 – 96 = 4

⇒ Loss % = (4/100) × 100 = 4%

∴  The loss percentage 4%.

13. A shopkeeper marks up the price of an article 60% above the C.P. and gives 10% discount, Find the profit %.

• 48
• 24
• 54
• 44

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Solution

Given:

Mark up% = 60%

Discount = 10%

Concept used:

Marked price = C.P. + Markup % of C.P.

Selling Price = Marked price – Discount

Profit % = S.P.−C.P.C.P.S.P.−C.P.C.P.* 100%

Calculations:

Let the C.P. of the article = 100x

Marked price = 100x + 60% of 100x 

 ⇒ Marked price = 160x

Selling price = 160x – 10% of 160x

 ⇒ Selling price = 160x – 16x

 ⇒ Selling price = 144x

Profit = 144x−100x100x144x−100x100x* 100 %

 ⇒ Profit = 44%

Hence option D is the correct answer.

14. The value of (113113 × 145145 ÷ 3535) × 3838 – 2323 is:

• 3232
• 1414
• 5656
• 7272

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Solution

Given:

(113113 × 145145 ÷ 3535) × 3838 – 2323

Concept used:

Calculation:

(113113 × 145145 ÷ 3535) × 3838 – 2323

⇒ (4343 × 9595 × 5353) × 3838 – 2323

⇒ 4 × 3838 – 2323

⇒ 3232 – 2323

⇒ 9−469−46

⇒ 5656

∴ Required answer is 5656.

15. In a factory 60% of the workers are above 30 years and of these 75% are males and the rest are females. If there are 1350 male workers above 30 years, the total number of workers in the factory is

• 3000
• 2000
• 1800
• 1500

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Solution

Let the total number of workers in the factory be X. Then,

Total number of workers above 30 years of age

=60100×X=60100×X

= 0.6X

Also it is given that out of these 75% are male. Thus

Total number of male workers above 30 years of age

=75100×(0.6X)=75100×(0.6X)

= 0.45X

It is given that total number of male workers above 30 years

= 1350

Hence,

⇒ 0.45X = 1350

⇒ X = 3000∴ Total workers in the factory are 3000.

• 300 Rs
• 200 Rs
• 600 Rs
• 500 Rs

16. The difference between two selling prices of a T-shirt with profits of 4% and 5% respectively is Rs. 6. Find C.P. of the T-shirt.

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Solution

Shortcut Trick5% of C.P – 4% of C.P = 6

⇒ 1 % of C.P = 6

⇒ 100 % of CP = 600

∴ Cost of T-shirt is 600 Rs.
Alternate Method

Formula used:

S.P. = C.P (1 + P%/100)

Calculation:

Using the above formula,

SP₁ = CP(1 + 4/100)

⇒ SP₁ = (26/25)C.P      —–(1)

SP₂ = (1 + 5/100)

⇒  SP₂ = (21/20)C.P      —–(2)

According to the question, 

SP₂ – SP₁ = 6

⇒ (21/20 – 26/25)C.P = 6

⇒ (105 – 104)C.P / 100 = 6

⇒ CP = 600 Rs.

∴ Cost of T-shirt is 600 Rs.

17. The value of 63 × 6 ÷ 54 – 11 ÷ 7 × 35 + 156 × 8 ÷ 13 – 9 ÷ 49 × 196 + 108 × 14 ÷ 36 is:

• 62
• 73
• 46
• 54

Solution

Given:

63 × 6 ÷ 54 – 11 ÷ 7 × 35 + 156 × 8 ÷ 13 – 9 ÷ 49 × 196 + 108 × 14 ÷ 36

Concept used:

Calculation:

63 × 6 ÷ 54 – 11 ÷ 7 × 35 + 156 × 8 ÷ 13 – 9 ÷ 49 × 196 + 108 × 14 ÷ 36

⇒ 63 × 1919 – 117117 × 35 + 156 × 813813 – 949949 × 196 + 108 × 718718

⇒ 7 – 55 + 96 – 36 + 42

⇒ 145 – 91

⇒ 54

∴ Required answer is 54.

18. It takes 8 people working at equal rates to finish a work in 96 days. How long will 6 workers take for the same work?

• 124 days
• 125 days
• 128 days
• 122 days

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Solution

Given:

8 people takes 96 days to complete the work

Concept used:

Total work = Number of men × Time taken

Calculation:

Total work = (8 × 96) units

Time taken by 6 worker = (8 × 96)/6 = 128 days

∴ 6 workers can do the same work in 128 days

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