SSC CGL 14 October 2025 · Shift 3 · Quantitative Aptitude — questions with answers · ShikshaSphere
Chapter 191 of 192
14 October 2025 · Shift 3
Quantitative Aptitude
25 questions ~25 min readFree
25 questions
A
51
Aman invested ₹60,000 for 10 months and Priya invested ₹90,000 for 8 months. If the total profit at the end of the year is ₹55,000, what is Priya's share in the profit?
A.₹25,000
B.₹28,000
C.₹30,000
D.₹32,500
Solution
Partnership
Aman: 60,000 × 10 = 6,00,000; Priya: 90,000 × 8 = 7,20,000.
Ratio = 600 : 720 = 5 : 6, a total of 11 parts.
Priya’s share = × 55,000.
= ₹30,000 — option (c).
52
Evaluate the continued fraction:
x = 3 +
A.
B.
C.
D.
Solution
Continued fraction
Start from the bottom: 6 + = .
Next: 8 + = 8 + = .
Finally: 3 + = 3 + .
= = — option (a).
53
Three classes have average ages 16, 18 and 21 respectively. The number of students in the three classes is in the ratio 3 : 4 : 5. What is the overall average age of all the students together?
A.18.7
B.19.2
C.17.8
D.20.1
Solution
Weighted average
Take the numbers as 3x, 4x and 5x, a total of 12x students.
Total age = 16(3x) + 18(4x) + 21(5x) = 48x + 72x + 105x = 225x.
Average = .
= 18.75 ≈ 18.7 — option (a).
54
From a 54-litre container of pure spirit, 9 litres are removed and replaced by water. This operation is performed a total of three times. What is the final quantity of spirit remaining in the container?
A.31.34 litres
B.36.45 litres
C.31.25 litres
D.42.88 litres
Solution
Repeated replacement
Each round leaves (1 − ) = of the spirit behind.
After three rounds the spirit left = 54 × ()³.
= 54 × .
= 31.25 litres — option (c).
55
In an election, 80% of eligible voters cast their votes. Of these votes, 5% were declared invalid. If the winning candidate received 22,800 votes, which accounted for 60% of the total valid votes, what was the total number of eligible voters?
A.40,000
B.50,500
C.50,000
D.40,500
Solution
Election votes
22,800 is 60% of the valid votes, so valid votes = = 38,000.
Valid votes are 95% of the votes cast, so votes cast = = 40,000.
Votes cast are 80% of the eligible voters.
Eligible = = 50,000 — option (c).
56
Radha invested ₹20,000 in a savings scheme that offers interest at 10% per annum, compounded annually. Find the compound interest earned by her at the end of 2 years and 6 months.
A.₹5,450
B.₹5,410
C.₹5,430
D.₹5,420
Solution
CI for a part year
For the two full years: 20,000 × ()² = ₹24,200.
For the remaining 6 months, simple interest is added: 24,200 × (1 + ) = 24,200 × .
= ₹25,410.
CI = 25,410 − 20,000 = ₹5,410 — option (b).
57
If a number x is subtracted from 52, 47, 20 and 19, the resulting numbers are in proportion. What is the value of x + 5?
A stationery shop ordered 16 dozen black pens and some additional dozens of blue pens. The price of the black pens per dozen was twice that of the blue ones. When the order was delivered, it was found that the number of dozens of the two colours had been interchanged. This increased the bill by 50%. Find the ratio of the number of dozens of black pens to the number of dozens of blue pens in the original order.
A.1 : 4
B.1 : 2
C.2 : 3
D.3 : 4
Solution
Interchanged order
Let the blue pens be m dozen and the price of a blue dozen be 1 unit, so a black dozen costs 2 units.
Original bill = 16(2) + m(1) = 32 + m; after the interchange = m(2) + 16(1) = 2m + 16.
The new bill is 1.5 times the old: 2m + 16 = (32 + m) ⇒ 4m + 32 = 96 + 3m ⇒ m = 64.
Ratio = 16 : 64 = 1 : 4 — option (a).
59
A cistern contains 100 litres of pure milk. 20 litres of milk are drawn out and replaced by water. Then 20 litres of the mixture are drawn out and replaced by water again. What is the ratio of water to milk in the final mixture?
A.18 : 1
B.9 : 16
C.16 : 9
D.1 : 18
Solution
Repeated replacement
Each round leaves (1 − ) = of the milk behind.
After two rounds the milk = 100 × ()² = 64 litres.
Water = 100 − 64 = 36 litres.
Water : milk = 36 : 64 = 9 : 16 — option (b).
Vinay and Ram can complete a task in 12 days and 18 days respectively. They begin the work together, but Ram leaves 4 days before the completion of the work. In how many days will the work finish?
A.5 days
B.8 days
C.1 days
D.8 days
Solution
Work with one leaving
Take the work as 36 units: Vinay does 3 a day and Ram 2 a day.
Let the whole job take n days. Vinay works all n days and Ram works (n − 4) days.
3n + 2(n − 4) = 36 ⇒ 5n − 8 = 36 ⇒ 5n = 44.
n = = 8 days — option (d).
62
In a triangle PQR, medians PS and QT intersect at O. If the length of median PS is 21 cm, what is the length of the segment PO?
A.14 cm
B.16 cm
C.10 cm
D.12 cm
Solution
Centroid divides a median
The point where the medians meet is the centroid.
The centroid divides every median in the ratio 2 : 1 from the vertex.
So PO = × PS = × 21.
= 14 cm — option (a).
63
A regular decagon can be divided into how many isosceles triangles by joining its vertices to its centre?
A.8
B.10
C.12
D.5
Solution
Polygon triangles
Joining the centre to every vertex creates one triangle for each SIDE of the polygon.
A decagon has 10 sides.
Each triangle has two radii as its equal sides, so all are isosceles.
= 10 — option (b).
64
A flagpole casts a shadow measuring 20 metres. Given that the height of the flagpole is 20 metres, at what angle is the sun elevated?
A spherical ball is submerged in water in a cylindrical container. The radius of the cylindrical container is 6 cm and its height is 35 cm. What is the volume of water displaced by the ball if its radius is 7 cm?
A.π cm³
B.π cm³
C.π cm³
D.π cm³
Solution
Water displaced
A fully submerged body displaces water equal to its own volume.
Volume of the sphere = πr³.
= π(7)³ = π.
= π cm³ — option (d).
66
Given x + y + z = 0, evaluate (x − y)³ + (y − z)³ + (z − x)³.
A.0
B.9(x − y)(y − z)(z − x)
C.27xyz
D.3(x − y)(y − z)(z − x)
Solution
Sum of cubes identity
If a + b + c = 0, then a³ + b³ + c³ = 3abc.
Here take a = x − y, b = y − z and c = z − x.
Their sum is (x − y) + (y − z) + (z − x) = 0, so the identity applies.
= 3(x − y)(y − z)(z − x) — option (d).
67
A right circular cone is cut parallel to its base, forming a frustum. The height of the original cone is 30 cm and the cut is made 6 cm from the top. What is the ratio of the volume of the frustum to the volume of the entire cone?
A.124 : 125
B.125 : 124
C.125 : 126
D.126 : 125
Solution
Frustum ratio
The small cone at the top is similar to the whole cone, with heights in the ratio = .
For similar solids the volumes are in the ratio of the CUBES of the heights.
Small : whole = 1³ : 5³ = 1 : 125, so the frustum takes up 125 − 1 = 124 parts.
Frustum : cone = 124 : 125 — option (a).
68
If tanA = and tanB = , with A and B in (0, ), find tan(A − B).
Slope of a line
Write the line in the form y = mx + c.
4y = −3x + 10 ⇒ y = −x + .
The coefficient of x is the slope.
= − — option (a).
70
If 75% of P = 60% of Q = 30% of R, find P : Q : R.
A.4 : 5 : 10
B.10 : 5 : 4
C.5 : 4 : 10
D.2 : 3 : 5
Solution
Ratio from percentages
Let each equal k: P = , Q = and R = .
So P : Q : R = : : .
Multiply throughout by 300: 4 : 5 : 10.
= 4 : 5 : 10 — option (a).
71
If a³ + b³ = 189 and ab = 20, find the value of a + b.
A.9
B.6
C.7
D.8
Solution
Sum of cubes
a³ + b³ = (a + b)³ − 3ab(a + b).
Let a + b = s: 189 = s³ − 60s.
s³ − 60s − 189 = 0; trying s = 9 gives 729 − 540 − 189 = 0 ✓.
a + b = 9 — option (a).
72
A point P is 17 cm away from the centre of a circle. A tangent drawn from P to the circle has a length of 15 cm. What is the circumference of the circle?
A.12π cm
B.15π cm
C.16π cm
D.18π cm
Solution
Tangent and circumference
The radius meets the tangent at right angles, giving a right triangle.
r = = = = 8 cm.
Circumference = 2πr.
= 16π cm — option (c).
73
A furniture shop first sells a dining chair for ₹X, thereby making a 25% profit. Later, for a festive period, the marked price of the same chair is raised to ₹1.8X and a discount of 20% is then given on this new marked price. What is the percentage profit earned by the store during the festive sale?
A.40%
B.80%
C.42%
D.70%
Solution
Festive-sale profit
A 25% profit means CP : SP = 4 : 5, so if X = 5 units then the cost price is 4 units.
New marked price = 1.8X = 1.8 × 5 = 9 units; after a 20% discount the selling price = 9 × 0.8 = 7.2 units.
Profit = 7.2 − 4 = 3.2 units on a cost of 4 units.
× 100 = 80% — option (b).
74
A right triangle has vertices at A(0, 0), B(10, 5) and C(2, 9). What are the coordinates of its circumcentre?
A.(6, 4)
B.(4, 7)
C.(4, 4)
D.(6, 7)
Solution
Circumcentre
The right angle is at A(0, 0), so BC is the hypotenuse.
In a right triangle the circumcentre lies at the midpoint of the hypotenuse.
Midpoint of B(10, 5) and C(2, 9) = (, ).
= (6, 7) — option (d).
75
Which of the following numbers is an integer but NOT a natural number?
A.3
B.0
C.6
D.9
Solution
Integers vs natural numbers
Natural numbers begin at 1: 1, 2, 3, …
Integers take in zero and the negatives as well.
Zero is therefore an integer but not a natural number.
3, 6 and 9 are both — option (b).
Finished reading? Now test yourself.
The same 25 questions, but with a timer and the answers hidden — 15 minutes.
Aman: 60,000 × 10 = 6,00,000; Priya: 90,000 × 8 = 7,20,000.
Ratio = 600 : 720 = 5 : 6, a total of 11 parts.
Priya’s share = × 55,000.
= ₹30,000 — option (c).
Start from the bottom: 6 + = .
Next: 8 + = 8 + = .
Finally: 3 + = 3 + .
= = — option (a).
Take the numbers as 3x, 4x and 5x, a total of 12x students.
Total age = 16(3x) + 18(4x) + 21(5x) = 48x + 72x + 105x = 225x.
Average = .
= 18.75 ≈ 18.7 — option (a).
Each round leaves (1 − ) = of the spirit behind.
After three rounds the spirit left = 54 × ()³.
= 54 × .
= 31.25 litres — option (c).
22,800 is 60% of the valid votes, so valid votes = = 38,000.
Valid votes are 95% of the votes cast, so votes cast = = 40,000.
Votes cast are 80% of the eligible voters.
Eligible = = 50,000 — option (c).
For the two full years: 20,000 × ()² = ₹24,200.
For the remaining 6 months, simple interest is added: 24,200 × (1 + ) = 24,200 × .
= ₹25,410.
CI = 25,410 − 20,000 = ₹5,410 — option (b).
In proportion: = .
Cross-multiplying: (52 − x)(19 − x) = (47 − x)(20 − x).
988 − 71x + x² = 940 − 67x + x² ⇒ 48 = 4x ⇒ x = 12.
x + 5 = 17 — option (c).
Let the blue pens be m dozen and the price of a blue dozen be 1 unit, so a black dozen costs 2 units.
Original bill = 16(2) + m(1) = 32 + m; after the interchange = m(2) + 16(1) = 2m + 16.
The new bill is 1.5 times the old: 2m + 16 = (32 + m) ⇒ 4m + 32 = 96 + 3m ⇒ m = 64.
Ratio = 16 : 64 = 1 : 4 — option (a).
Each round leaves (1 − ) = of the milk behind.
After two rounds the milk = 100 × ()² = 64 litres.
Water = 100 − 64 = 36 litres.
Water : milk = 36 : 64 = 9 : 16 — option (b).
Take the work as 36 units: Vinay does 3 a day and Ram 2 a day.
Let the whole job take n days. Vinay works all n days and Ram works (n − 4) days.
3n + 2(n − 4) = 36 ⇒ 5n − 8 = 36 ⇒ 5n = 44.
n = = 8 days — option (d).
The point where the medians meet is the centroid.
The centroid divides every median in the ratio 2 : 1 from the vertex.
So PO = × PS = × 21.
= 14 cm — option (a).
Joining the centre to every vertex creates one triangle for each SIDE of the polygon.
A decagon has 10 sides.
Each triangle has two radii as its equal sides, so all are isosceles.
= 10 — option (b).
tanθ = .
= = .
tanθ = gives θ = 60°.
Hence option (c).
A fully submerged body displaces water equal to its own volume.
Volume of the sphere = πr³.
= π(7)³ = π.
= π cm³ — option (d).
The small cone at the top is similar to the whole cone, with heights in the ratio = .
For similar solids the volumes are in the ratio of the CUBES of the heights.
Small : whole = 1³ : 5³ = 1 : 125, so the frustum takes up 125 − 1 = 124 parts.
Frustum : cone = 124 : 125 — option (a).
tan(A − B) = .
Numerator = − = .
Denominator = 1 + = .
= — option (b).
Write the line in the form y = mx + c.
4y = −3x + 10 ⇒ y = −x + .
The coefficient of x is the slope.
= − — option (a).
Let each equal k: P = , Q = and R = .
So P : Q : R = : : .
Multiply throughout by 300: 4 : 5 : 10.
= 4 : 5 : 10 — option (a).
a³ + b³ = (a + b)³ − 3ab(a + b).
Let a + b = s: 189 = s³ − 60s.
s³ − 60s − 189 = 0; trying s = 9 gives 729 − 540 − 189 = 0 ✓.
a + b = 9 — option (a).
The radius meets the tangent at right angles, giving a right triangle.
r = = = = 8 cm.
Circumference = 2πr.
= 16π cm — option (c).
A 25% profit means CP : SP = 4 : 5, so if X = 5 units then the cost price is 4 units.
New marked price = 1.8X = 1.8 × 5 = 9 units; after a 20% discount the selling price = 9 × 0.8 = 7.2 units.
Profit = 7.2 − 4 = 3.2 units on a cost of 4 units.
× 100 = 80% — option (b).
The right angle is at A(0, 0), so BC is the hypotenuse.
In a right triangle the circumcentre lies at the midpoint of the hypotenuse.
Midpoint of B(10, 5) and C(2, 9) = (, ).
= (6, 7) — option (d).