Mathematics is an integral part of various competitive exams, including the OSSSC (Odisha Subordinate Staff Selection Commission) RI (Revenue Inspector), ARI (Assistant Revenue Inspector), Amin, SFS, and ICDSSupervisor exams. To excel in these exams, candidates need to have a solid understanding of mathematical concepts and problem-solving skills. To help you prepare effectively, we’ve compiled a list of the top 30 Mathematics Multiple Choice Questions (MCQs) commonly encountered in these exams.
Top 30 Mathematics MCQs For OSSSC RI,ARI, Amin, SFS, ICDS Supervisor
- a number exceeds another number by 5.the sum of the numbers is 19. find the smaller number ?
A. 5
B. 6
C. 7
D. 12
Ans: D. 12
Let one of the numbers be “x”; then the other is “x+5”.
Equation:
x + x+5 = 19
2x = 14
x = 7 (the 1st number)
x+5 = 12 (the other number) - Hafeez invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Hafeez at the end of the year will be?
A. Rs. 16,500
B. Rs. 16,525.50
C. Rs. 16,537.50
D. Rs. 18,150
Ans: C. Rs. 16,537.50
Explanation:
P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20) = Rs. 16537.50 - The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree, is :________?
A. 30°
B. 45°
C. 60°
D. 90°
Ans: A. 30°
Let AB be the tree and AC be its shadow.
Let ∠ACB = θ.
Then, AC/AB = √3
Cot θ = √3
θ = 30° - 18 men can eat 20 kg of rice in 3 days. How long will 6 men take to eat 40 kg of rice?
A. 20
B. 18
C. 32
D. 20
Ans: B. 18
18*3/20=6/40x
54/20=6/40x
54*40/20*6=x
18=x - A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
A. 2:3:5
B. 3:4:7
C. 4:5:9
D. None of these
Ans: B. 3:4:7
Explanation:
A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7 - A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full the leak will empty it in.
A. 16 hrs
B. 20 hrs
C. 25 hrs
D. 40 hrs
Ans: D. 40 hrs
Work done by leak in 1 hour = (1/8 – 1/10) = 1/40
The leak will empty the cistern in 40 hours. - Three flags each of different colours are available for a military exercise, Using these flags different codes can be generated by waving
I. Single flag of different colours
II. Any two flags in a different sequence of colours.
III. three flags in a different sequence of colours.
The maximum number of codes that can be generated is.
A. 6
B. 9
C. 15
D. 18
Ans: C. 15
Explanation:
This type of question becomes very easy when we assume three colour are red(R) blue(B) and Green(G).
We can choose any colour.
Now according to the statement 1 i.e.., codes can be generated by waving single flag of different colours, then number of ways are three i.e.., R.B.G from statement III three flags in different sequence of colours, then number of ways are six i.e.., RBG, BGR, GBR, RGB, BRG, GRB.
Hence total number of ways by changing flag = 3+ 6 +6 = 15 - A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:_________?
A. Rs.50
B. Rs.60
C. Rs.80
D. Rs.90
Ans: C. Rs.80
Explanation:
Let C.P. of clock be Rs. x.
Then, C.P. of 90 clocks = Rs. 90x.
[(110% of 40x) + (120% of 50x)] – (115% of 90x) = 40
44x + 60x – 103.5x = 40
0.5x = 40 => x = 80 - The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:__________?
A. 51:52
B. 52:53
C. 51:53
D. 52:55
Ans: B. 52:53
Explanation:
Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53 - If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:________?
A. Rs. 50
B. Rs. 160
C. Rs. 200
D. Rs. 225
Ans: C. Rs. 200
Explanation:
Let C.P. be Rs. x.
Then, 5% of x = 350 – 340 = 10
x/20 = 10 => x = 200 - In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
A. 50
B. 40
C. 25
D. 15
Ans: C. 25
Explanation:
A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 – 75) = 25 points to C. - In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
A. 57.5 m
B. 127.5 m
C. 150.7 m
D. 98.6 m
Ans: B. 127.5 m
Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 – 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m. - A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?
A. 432
B. 288
C. 144
D. 72
Ans: C. 144
Explanation:
Let the number of coins of each kind be x.
=> 5x + 2x + 1x = 1152
=> 8x = 1152 => x = 144 - Arslan and Bilal have some marbles with them. Arslan told Bilal “if you give me ‘x’ marbles, both of us will have equal number of marbles”. Bilal then told Arslan “if you give me twice as many marbles, I will have 30 more marbles than you would”. Find ‘x’?
A. 4
B. 5
C. 6
D. 8
Ans: B. 5
Explanation:
If Bilal gives ‘x’ marbles to Arslan then Bilal and Arslan would have V – x and A + x marbles.
V – x = A + x — (1)
If Arslan gives 2x marbles to Bilal then Arslan and Bilal would have A – 2x and V + 2x marbles.
V + 2x – (A – 2x) = 30 => V – A + 4x = 30 — (2)
From (1) we have V – A = 2x
Substituting V – A = 2x in (2)
6x = 30 => x = 5. - A man buys Rs. 25 shares in a company which pays 9% dividend . The money invested is such that it gives 10% on investment. At what price did he buy the shares?
A. Rs.22
B. Rs.22.50
C. Rs.25
D. Rs.22.50
Ans: B. Rs.22.50
Suppose he buys each share be Rs. X.
Then, (25 x 9/100)=(X x 10/100) X= 22.50
Cost of each share is Rs. 22.50. - Find the cost of 96 shares of Rs. 10 each at (3/4) discount, brokerage being(1/4) per share.
A. 812
B. 912
C. 1012
D. 1112
Ans: B. 912
Cost of 1 share = Rs. [(10-(3/4)) + (1/4)] = Rs. (19/2).
Cost of 96 shares = Rs. [(19/2)*96] = Rs. 912. - An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
A. 4 : 3
B. 8 : 7
C. 4 : 1
D. 6 : 5
Ans: B. 8 : 7
Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6×2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7 - The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
A. 91.5 cm
B. 93.5 cm
C. 94.5 cm
D. 92.5 cm
Ans: A. 91.5 cm
Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm - The length of a rectangle is two – fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
A. 140
B. 156
C. 175
D. 214
Ans: A. 140
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units - The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
A. 81 : 121
B. 9 : 11
C. 729 : 1331
D. 27 : 12
Ans: A. 81 : 121
Ratio of the sides = ³√729 : ³√1331 = 9 : 11
Ratio of surface areas = 92 : 112 = 81 : 121 - 6 of 5/8 / 5/8 – 1/8 = ______?
A. 6 1/8
B. 5 3/4
C. 6 3/4
D. 5 7/8
Ans: D. 5 7/8
Explanation:
6 of 5/8 / 5/8 – 1/8
30/8 * 8/5 – 1/8 = 6 – 1/8 = 5 7/8 - (22 * 495 + 891 * 44) / (33 * 176 + 55 * 264) = _________?
A. 1
B. 2
C. 69/28
D. 66/17
Ans: C. 69/28
Explanation:
(22 * 495 + 891 * 44) / (33 * 176 + 55 * 264) = (22 * 33 * 15 + 9 * 99 * 2 * 22) / (33 * 22 * 8 + 5 * 11 * 22 * 12)
= (22 * 33 * 15 + 22 * 33 * 54) / (33 * 22 * 8 + 33 * 22 * 20) = [22 * 33(15 + 54)] / [33 * 22(8 + 20)] = 69/287 + 5 – (3/2 * 1/4) of 2/7 + 7/2 * 1/6 equals ________.
A. 12 3/88
B. 24 21/24
C. 12 25/224
D. 12 1/224
Ans: C. 12 25/224
Explanation:
7 + 5 – (3/2 * 1/4) of 2/7 + 7/2 * 1/16
= 7 + 5 – (3/2 * 1/4) * 2/7 + 7/2 * 1/16 = 7 + 5 – 3/28 + 7/32
= 12 + 3/28 + 7/32 = 12 + (7 * 7 – 3 * 8)/224
= 12 + 25/224 = 12 25/224 - A boat having a length 3 m and breadth 2 m is floating on a lake The boat sinks by 1 cm when a man gets on it. The mass of man is :__________?
A. 12 kg
B. 60 kg
C. 72 kg
D. 96 kg
Ans: B. 60 kg
Volume of water displaced = (3 X 2 X 0.01) m3 = 0.06 m3.
Mass of man = Volume of water displaced X Density of water
= (0.06 X 1000) kg = 60 kg. - The areas of the three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to :___________?
A. the volume of the box
B. twice the volume of the box
C. the square of the volume of the box
D. the cube root of the volume of the box
Ans: C. the square of the volume of the box
Let length = 1, breadth = b and height = h. Then,
Product of areas of 3 adjacent faces = (lb x bh x 1h) = (lbh)2 = (Volume)2. - A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the joɡɡer?
A. 3.6 sec
B. 18 sec
C. 36 sec
D. 72 sec
Ans: C. 36 sec
Explanation
With 5 best steps
1.Data:
Speed 1=V₁= 9km/h
Distance 1=S₁= 240 m
Distance 2 =S₁= 120 m
Speed 2=V₂= 45km/h
Relative speed(V) = V₂_V₁
Relative speed (V)= 45km/h_9 km/h
Relative speed (V)=36km/h
Relative speed(V)= 36×1000m/3600Sec
Relative speed (V)= 36000m/3600Sec
Relative speed(V)= 10 m/sec
Covered distance(S)= 240m+120m
Covered distance (S)= 360m.
2. Required:
Time taken= T=??
3. Formula:
S= V×T
For T
T = S/V
4. Solution:
Putting values in formula.
T= 360 m/10 m/Sec
T= 36Sec
5. Result:
Time taken= T= 36 Sec - Two trains are moving in opposite directions 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is_________?
A. 36
B. 45
C. 48
D. 49
Ans: C. 48
Explained with 5 Steps.
1.Data:
Speed 1 = 60 km/hr
Speed 2= 90 km/hr
Relative speed= (60+90)km/hr
Relative speed= 150 km/hr
Relative speed= 150×1000m/3600 Sec
Relative speed= 150,000m/3600 Sec
Relative speed= 1500m/36Sec
Relative speed= 42m/Sec
Distance 1= 1.10km
Distance 2= 0.9km
Total distance= (1.10+0.9) km
D(t)= 2 km => 2×1000m
D(t) = 2000m
2 Required:
Time=T=???
3. Formula:
S = V×T
For T
T= S/V
4. Solution:
Putting value in formulas.
T= 2000m/ 42 m/sec
T= 48Sec
5. Result:
Time =T= 48 Sec - In what ratio should the profit be divided if M, N, O invests capital in ratio 2:3:5 and their timing of their investments are in the ratio 4:5:6.
A. 8:15:30
B. 5:18:28
C. 4:5:6
D. 2:3:5
Ans: A. 8:15:30
P1:P2:P3 = (2*4):(3*5):(5*6)
= 8 : 15 : 30 - If Ahmed purchases a Watch for Rs 600 and pays 15% sales tax, the total amount spent on purchase is?
A. 660
B. 670
C. 680
D. 690
E. 700
Ans; D. 690
If Ahmed purchases a Watch for and pays sales tax, the total amount spent on purchase is 690.
EXPLANATION
= 600x(1+15%)
= 600×1.15
= 690 - From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is_________?
A. 1/26
B. 3/52
C. 15/26
D. 11/26
Ans: A. 1/26
Explanation:
Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26 - Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
A. 1/6
B. 5/8
C. 3/8
D. 5/6
Ans: D. 5/6
Explanation:
P(at least one graduate) = 1 – P(no graduates) =
1 – ⁶C₃/¹⁰C₃ = 1 – (6 * 5 * 4)/(10 * 9 * 8) = 5/6
