SSC CGL 24th August Shift 2 - QA
Avinash has 20% less coins of different countries than Gaurav has. Gaurav has 40% more such coins than Chetan has. By what percent the number of coins which Chetan hasis less than the number of coins which Avinash has? (correct to one decimalplace)
- A.
10.7
- B.
10.6
- C.
10.5
- D.
12
Answer: Option A
Explanation :
Workspace:
If x - = 15, then what is the value of ?
- A.
229
- B.
227
- C.
221
- D.
223
Answer: Option A
Explanation :
x - = 15
Squaring on both sides,
x² + - 2.x. = 225
x² + - 4 = 225
x² + = 229
Hence, the correct answer is Option A
Workspace:
Simplify the following expression:
÷ of - × + ÷ of
- A.
8
- B.
-4
- C.
3
- D.
7
Answer: Option A
Explanation :
÷ of - × + ÷ of
= ÷ - × + ÷
= ÷ - × + ×
= - +
=
=
=
= 8
Hence, the correct answer is Option A
Workspace:
The data given in the table shows the number of boys and girls enrolled in three different streams in a school over 5 years.
What is the ratio of the total number of boys in the year 2014 to the total number of girls in the year 2020?
- A.
58 : 57
- B.
55 : 57
- C.
58 : 53
- D.
1 : 1
Answer: Option A
Explanation :
Workspace:
If sin² θ = 2 sin θ - 1, 0° ≤ θ ≤ 90°, then find the value of:
- A.
-2
- B.
1
- C.
2
- D.
-1
Answer: Option C
Explanation :
sin² θ = 2 sin θ - 1
sin² θ - 2 sin θ + 1 = 0
(sin θ - 1)² = 0
sin θ - 1 = 0
sin θ = 1
0° ≤ θ ≤ 90°
⇒ θ = 90°
=
=
= 2
Hence, the correct answer is Option C
Workspace:
In △ABC and △DEF we have = = then which of the following is true?
- A.
△BCA∼△DEF
- B.
△DEF∼△ABC
- C.
△DEF∼△BAC
- D.
△CAB∼△DEF
Answer: Option A
Explanation :
Hence, the correct answer is Option A
Workspace:
In a circle with centre O, AB is a chord of length 10 cm. Tangents at points A and B intersect outside the circle at P. If OP = 2 OA, then find the length (in cm) of AP.
- A.
12.5
- B.
10
- C.
12
- D.
15
Answer: Option B
Explanation :
Workspace:
Monthly salaries of Anil and Kumud are in the ratio 19 : 17. If Anil and Kumud get salary hike of ₹2000 and ₹1000 respectively, then the ratio in their salaries become 8 : 7. What is the present salary of Kumud(in ₹)?
- A.
38000
- B.
18000
- C.
34000
- D.
35000
Answer: Option C
Explanation :
Monthly salaries of Anil and Kumud are in the ratio 19 : 17.
Let the monthly salaries of Anil and Kumud are 19p and 17p respectively.
Anil and Kumud get salary hike of ₹2000 and ₹1000 respectively, then the ratio in their salaries become 8 : 7.
=
133p + 14000 = 136p + 8000
3p = 6000
p = 2000
Present salary of Kumud = 17p = ₹34000
Hence, the correct answer is Option C
Workspace:
Trader A gives a single discount of 25% and Trader B gives two successive discounts of 20% and 5% on an identical item. If the discount given by A is ₹320 more than the discount given by B, then what is the marked price (in ₹) of the item?
- A.
3200
- B.
32000
- C.
30000
- D.
25000
Answer: Option B
Explanation :
Let the marked price of the item = M
i) Trader A gives a single discount of 25%.
Discount = M = M
ii) Trader B gives two successive discounts of 20% and 5%.
Price of the item after 20% discount = × M
Price of the item after 5% discount = × × M = M
Total discount given trader B = M - M = M
According to the problem, discount given by A is ₹320 more than the discount given by B.
M = M + 320
= 320
M = ₹32000
Hence, the correct answer is Option B
Workspace:
Eighteen men can complete a work in 14 days. Three women do as much work as two men. Five men and six women started the work and continued for 4 days. Subsequently 3 more men joined the group. In how manytotal days was the work completed?
- A.
21
- B.
17
- C.
18
- D.
22
Answer: Option D
Explanation :
Workspace:
The value of
is:
- A.
-3(2 + )
- B.
3(2 - )
- C.
-3(2 - )
- D.
3(2 + )
Answer: Option A
Explanation :
=
=
=
= ×
=
= -3(2 + )
Workspace:
Simplify the following expression.
- A.
(a³ - b³)(b³ - c³)(c³ - a³)
- B.
(a³ - b³)(b³ + c³)(c³ + a³)
- C.
(a³ - b³)(b³ - c³)(c³ + a³)
- D.
(a³ + b³)(b³ + c³)(c³ + a³)
Answer: Option D
Explanation :
Workspace:
Atul borrowed a sum of ₹12000 and agreed to repay it by paying ₹4800 at the end of first year and ₹9240 at the end of second year. Whatis the rate of compound interest compounded annually?
- A.
10%
- B.
8%
- C.
12%
- D.
%
Answer: Option A
Explanation :
Workspace:
What is the product of the average of first ten positive odd numbers and the average of first fifteen positive even numbers?
- A.
44
- B.
150
- C.
160
- D.
85.25
Answer: Option C
Explanation :
Workspace:
Bar graph shows the number of males and females in five organizations A, B, C, D and E.
What is the ratio of number of males working in organizations C, D and E taken together to that of females working in organizations A, B and C taken together?
- A.
10 : 11
- B.
49 : 46
- C.
11 : 10
- D.
46 : 49
Answer: Option A
Explanation :
Number of males working in organizations C, D and E taken together = 325 + 275 + 150 = 750
Number of females working in organizations A, B and C taken together = 300 + 275 + 250 = 825
Required ratio = 750 : 825
= 10 : 11
Hence, the correct answer is Option A
Workspace:
A shop keeper sold an article at four-fifth of the marked price and suffered a loss of 3 %. Find the profit percent, if he sold the article at the marked price.
(correct to nearest integer)
- A.
22
- B.
18
- C.
21
- D.
20
Answer: Option C
Explanation :
Let the cost price of the article = 100C
Loss = =
Selling price of the article = 100C - × 100C
= C
Shop keeper sold the article at four-fifth of the marked price.
C = × Marked price of the article
Marked price of the article = C
Profit percentage when article is sold at marked price = × 100
= × 100
= 20.833%
= 21% (approximately)
Hence, the correct answer is Option C
Workspace:
Points A, B and C are on circle with centre O such that ∠BOC = 84°. If AC is produced to a point D such that ∠BDC = 40°, then find the measure of ∠ABC (in degrees).
- A.
98
- B.
92
- C.
56
- D.
102
Answer: Option A
Explanation :
Angle subtended by chord BC at the centre is twice the angle subtended by chord BC on the point A of the circle.
∠BOC = 2∠BAC
84° = 2∠BAC
∠BAC = 42°
From triangle BAD,
∠BAD + ∠ABD + ∠BDA = 180°
42° + ∠ABD + 40° = 180°
∠ABD = 98°
Hence, the correct answer is Option A
Workspace:
A man walking at a speed of 3 km/h crosses a square field diagonally in 5 minutes. What is the area of the field (in m²)?
- A.
31250
- B.
3125
- C.
312.5
- D.
3.125
Answer: Option A
Explanation :
Let the side of the square field = a
Speed of the man = 3 km/h = 3 x m/min = 50 m/min
Time taken to cross the field diagonally = 5 minutes
Length of the diagonal of the square field = 50 x 5 = 250 m
a = 250
a = m
Area of the square field =
=
=
= 31250 m²
Hence, the correct answer is Option A
Workspace:
If y = 2x + 1, then what is the value of (8x3 - y3 + 6xy)?
- A.
1
- B.
-1
- C.
15
- D.
-15
Answer: Option B
Explanation :
y = 2x + 1
2x - y = -1 ...(1)
Cubing on both sides, we get
8x3 - y3 -3.2x.y(2x - y) = -1
8x3 - y3 - 6xy(-1) = -1 [From (1)]
8x3 - y3 + 6xy = -1
Hence, the correct answer is Option B
Workspace:
The pie graph shows the distribution of employees working in five departments A, B, C, D and E of a company.
Total number of employees = 9000
If the number of employees working in department A is x and the total number of employees working in departments C and E is y, then the value of y - 2x is:
- A.
725
- B.
850
- C.
1000
- D.
915
Answer: Option D
Explanation :
Number of employees working in department A = x = × 9000 = 1605
x = 1605
Number of employees working in department C = × 9000 = 1800
Number of employees working in department E = × 9000 = 2325
The total number of employees working in departments C and E = y = 1800 + 2325 = 4125
y = 4125
y - 2x = 4125 - 2(1605) = 4125 - 3210 = 915
Hence, the correct answer is Option D
Workspace:
Places A and are 45 km apart from each other. A car starts from place A and another car starts from place at the same time. If they move in the same direction, they meet in 4 and a half hour and if they move towardseach other, they meet in 27 minutes. Whatis the speed (in km/h) of the car which moves faster?
- A.
56
- B.
55
- C.
45
- D.
50
Answer: Option B
Explanation :
Workspace:
Points M and N are on the sides PQ and QR respectively of a triangle PQR. right angled at Q. If PN = 9 cm, MR = 7 cm, and MN = 3 cm, then find the length of PR (in cm).
- A.
11
- B.
13
- C.
12
- D.
Answer: Option A
Explanation :
From right angled triangle QMN,
b2 + c2 = 32
b2 + c2 = 9..........(1)
From right angled triangle PQN,
(a + b)2 + c2 = 92
a2 + b2 + 2ab + c2 = 81
a2 + 2ab + 9 = 81 [From (1)]
a2 + 2ab = 72..........(2)
From right angled triangle MQR,
b2 + (c + d)2 = 72
b2 + c2 + d2 + 2cd = 49
9 + d2 + 2cd = 49 [From (1)]
d2 + 2cd = 40..........(3)
From right angled triangle PQR,
(a + b)2 + (c + d)2 = PR2
a2 + 2ab + b2 + c2 + d2 + 2cd = PR2
72 + 9 + 40 = PR2
PR2 = 121
PR = 11 cm
Hence, the correct answer is Option A
Workspace:
Find the sum of all the possible values of (a + b), so that the number 4a067b is divisible by 11.
- A.
21
- B.
11
- C.
16
- D.
5
Answer: Option A
Explanation :
Workspace:
Find the value of sin2 60° + cos2 30° - sin2 45° - 3 sin2 90°.
- A.
- B.
-1
- C.
-1
- D.
-2
Answer: Option D
Explanation :
sin2 60° + cos2 30° - sin2 45° - 3 sin2 90° = + - - 3(1)²
= + - - 3
=
=
= -2
Hence, the correct answer is Option D
Workspace:
The bar graph given below shows the sales of Newspapers (in lakh number) from six branches of a Media Publication Company during two consecutive years 2017 and 2018.
(Note: The data shown below is only for mathematical exercise. They do not represent the actual figures).
Total Sales of U for both the years is what percent (correct to one place of decimal) of the combined Sales of the branches Q and R for 2017 and 2018?
- A.
48.6%
- B.
67.1%
- C.
44.4%
- D.
41.0%
Answer: Option C
Explanation :
Total Sales of U for both the years = 80 + 100
= 180
Total sales of Q for 2017 and 2018 = 85 + 85
= 170
Total sales of R for 2017 and 2018 = 105 + 130
= 235
The combined Sales of the branches Q and R for 2017 and 2018 = 170 + 235
= 405
Required percentage = × 100
= 44.4%
Hence, the correct answer is Option C
Workspace: