SSC CGL solved question paper Tier-I exam held on 31stAug 2016: Quantitative Aptitude
In this article, you will find 25 solved questions of Aptitude section asked in SSC CGL tier-1 exam held on 31stAugust, 2016 (Morning shift) with appropriate questions analysis-
In this article, you will get 25 solved questions of Aptitude section asked in SSC CGL tier-1 exam held on 31stAugust, 2016 (Morning shift). Please find the topic wise questions distribution in the examination in the table described below-
No. of questions
Simple and Compound Interest
Profit, Loss, and Discount
Time and Distance
Time and Work
From the above table, we can find that higher number of questions were asked from Algebra, Geometry, Data Interpretation, Mensuration, and Trigonometry. The level of questions was a bit difficult and time-consuming. Hence, we recommend you to allocate more time on these topics to score high in upcoming SSC CGL exam. So, Let us go through these questions-
Question 1.A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, the time A alone will take to finish the work is
a. 4 days
b. 6 days
c. 8 days
d. 12 days
Ans. 12 days
Explanation: (A + B)’s efficiency= 100/9 (= 11.11%).
Suppose, the efficiency of B= x%; hence, the efficiency of A= 3x;
x + 3x= 100/9; x= (25/9)%. => The efficiency of A= (25/3)%.
A will do this work in = 100/(25/3) = 12 days;
Question 2.The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is
Explanation: Volume1: Volume2 = (pi*r12h1): (pi* r22h2);
Since, volumes of both cylinders are equal;
(r1/r2)2=(h2/h1); => h1/h2 =4: 9;
Question 3.A trader sold a cycle at a loss of 10%. If the selling price had been increased by Rs. 200, there would have been a gain of 6%. The cost price of the cycle is
Explanation: Suppose that the cost price of the cycle= Rs. x;
x -----(sold at a loss of -10% )----> 0.90x;
0.90x------------(Rs. 200 increase)------> 0.90x + 200;
As per the stated condition,
0.90x + 200 = 1.06x;
x = Rs. 1250;
Question 4.In a city, 40% of the people are illiterate and 60% are poor. Among the rich, 10% are illiterate. The percentage of the illiterate poor population is
Explanation: Let Total number of people =100;
Total poor people = 60% of 100 =(60*100)/100=60=(60*100)/100=60;
Therefore, rich people = 40% of 100 =(40*100)/100=40=40;
Total illiterate people = 40% of total people =(40*100)/100=40;
Among rich, 10% are illiterate = 10% of 40 =(10*100)/40=4;
The number of the illiterate poor population =40−4=36;
Therefore, illiterate poor =36, total population =100;
Required percentage =(36*100)/100=36%.
Question 5.In what time will a 100 metres long train running with a speed of 50 km/hr cross a pillar?
a. 7.0 sec
b. 72 sec
c. 7.2 sec
d. 70 sec
Ans. 7.2 sec
Explanation: Speed = Distance/Time;
Time= Distance/ Speed; => Time = 100/(50*5/18) = 7.2 sec.
Question 7.If l + m + n = 9 and l2 + m2 + n2 = 31, then the value of lm + mn + nl will be
Explanation: (l + m + n)2= l2 + m2 + n2+2(l*m + m*n + n*l);
Hence, lm + mn + nl = 92 – 31 = 50/2= 25;
Question 8.The centroid of a triangle is the point where
a. the medians meet
b. the altitudes meet
c. the right bisectors of the sides of the triangle meet
d. the bisectors of the angles of the triangle meet
Ans. the medians meet
Explanation: in the following figure, O is the centroid of the triangle.
Question 9.In a triangle PQR, the side QR is extended to S. ∠QPR = 72° and ∠PRS = 110°, then the value of ∠PQR is:
Question 10.In a trapezium ABCD, AB || CD, AB < CD, CD = 6 cm and distance between the parallel sides is 4 cm. If the area of ABCD is 16 cm2, then AB is
a. 1 cm
b. 2 cm
c. 3 cm
d. 8 cm
Ans. 2 cm
Explanation: The area of trapezium = ½ * Sum of the parallel sides* uniform altitude;
Let AB = x cm;
16 = ½ *(6 + x)* 4; => x = 2cm;
Question 11.If tanθ + cotθ = 5, then the value of tan2 θ+ cot2 θ is
Explanation: tanθ + cotθ = 5; (given)
Square both sides-
tan2 θ+ cot2 θ + 2 = 25;
tan2 θ+ cot2 θ = 23;
Question 12.When a number is divided by 56, the remainder will be 29. If the same number is divided by 8, then the remainder will be
Explanation: Let the dividend be x;
Then the number will be= 56x + 29;
When the above expression will be divided by 8, then the remainder will be equal to (29%8 = 5)
Question 13.If a shop keeper marks his goods for a certain amount so as to get 25% gain after allowing a discount of 20%, then his marked price is
Explanation: Let the Marked price = Rs. x;
The selling price = 0.80x;
So, the cost price = 0.75*0.80*x;
Let the cost price of the item is Rs. 100.
Hence, 0.75*0.80*x = 100;
Question 14.The average of marks of 17 students in an examination was calculated as 71. But it was later found that the mark of one student had been wrongly entered as 65 instead of 56 and another as 24 instead of 50. The correct average is
Explanation: The total marks obtained by the students= 71* 17= 1207;
After correction, The total marks obtained= 1207 – 65 + 56 -20 +50= 1228;
The average of marks obtained by the students= 1228/ 17 = 72.23;
Question 15.The simple interest on a sum for 5 years is two-fifth of the sum. The rate of interest per annum is
SI= 2/5 * P;
R= (2/5 * 100)/5 = 8%= 0.08.
Question 17.If a - b = 3 and a2 + b2 = 25, then the value of ab is
Question 18.In ΔABC, ∠B = 70°and ∠C = 60°. The internal bisectors of the two smallest angles of ΔABC meet at O. The angle so formed at O is
Question 19.If θ be positive acute angle and 5cosθ + 12sinθ = 13, then the value of cosθ is
Explanation: 5cosθ + 12sinθ = 13;
(5/13) * cosθ + (12/13) * sinθ = 1;
Suppose that the angle formed in the figure is ∅.
sin(θ + ∅)= sin90;
θ + ∅ = 90;
θ =90- ∅;
cos θ= cos(90- ∅);
cos θ=sin∅= 5/13;
Question 20.A cylinderical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, what is the radius of its base?
a. 12 cm
b. 24 cm
c. 36 cm
d. 48 cm
Ans. 36 cm
Explanation: The volume of both the shapes are same.
Pi* (18)2* 32= 1/3 * pi* r2* 24;
R= 36 cm.
Question 21.The angle of elevation of the top of a pillar from the foot and the top of a building 20 m high, are 60° and 30° respectively. The height of the pillar is
a. 10 m
c. 60 m
d. 30 m
Ans. 30 m
In Triangle ACD, tan60= h/x;
In Triangle ABE, tan30= (h-20)/x;
Divide both the expression,
tan60/tan30 = (h/x)/(h-20/x);
h/h-20= 3; => h= 30 m;
Question 22.The pie-chart shows the percentage of literate and illiterate male and female in a state. Study the diagram and answer the following questions.
If the total number is 35000, then the difference between the numbers of literate male and literate female is
Explanation: Percentage change in literate male and female= 45 – 35 = 10%.
Hence, the required answer = 35000*10%= 3500.
Question 23.The pie-chart shows the percentage of literate and illiterate male and female in a state. Study the diagram and answer the following questions.
The difference of central angles corresponding to illiterate male and illiterate female is
Explanation: Percentage change in illiterate male and female= 12 – 8 = 4%.
Hence the required angle= 360*4%= 14.4.
Question 24.The pie-chart shows the percentage of literate and illiterate male and female in a state. Study the diagram and answer the following questions.
If the difference between the two categories of people are represented by 36° in the diagram then these categories are
a. literate male and literate female
b. literate male and illiterate male
c. illiterate male and literate female
d. illiterate male and illiterate female
Ans. literate male and literate female
Explanation: for this angle, the difference should be= 10%.
By observation, Literate male and literate female have this difference accurately.
Question 25.The pie-chart shows the percentage of literate and illiterate male and female in a state. Study the diagram and answer the following questions.
If two categories together have a central angle of 169.20,then these categories are
a. literate female and illiterate female
b. literate male and illiterate female
c. illiterate male and illiterate female
d. illiterate male and literate female
Ans. literate female and illiterate female
Explanation: For this angle, required percentage = 169.2*100/360= 47%.
This would be the = sum of literate female and illiterate male;