Ratio & Proportion · SSC CGL previous year questions

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2025 111 questions

Q632025 · 18 Sept 2025 · Shift 2
A cone is sliced into two sections by a plane that is parallel to its base, with the upper section representing 1/8 of the overall volume. What is the ratio of the heights of the smaller cone to the original cone?
1. A.1 : 2
2. B.1 : 7
3. C.5 : 1
4. D.6 : 1
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Answer: A
Q672025 · 18 Sept 2025 · Shift 2
A sector of a circle has a central angle of $12 0^{\circ}$ and a radius of 5 cm. Another sector of the same circle has a central angle of $\frac{2 π}{3}$ radians. What is the ratio of the area of the first sector to the area of the second sector?
1. A.1 : 1
2. B.3 : 4
3. C.2 : 3
4. D.5 : 6
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Answer: A
Q692025 · 18 Sept 2025 · Shift 2
In a trapezoid, the two parallel sides are in the ratio 3 : 5. If the height of the trapezoid is 10 cm and its total area is 240 cm², determine the lengths of the parallel sides.
1. A.15 cm and 25 cm
2. B.18 cm and 30 cm
3. C.20 cm and 40 cm
4. D.30 cm and 50 cm
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Answer: B
Q542025 · 18 Sept 2025 · Shift 3
Two containers of equal capacity are filled with milk and water. The first contains milk and water in the ratio 2 : 3, and the second in the ratio 3 : 2. The mixtures are then combined. What is the ratio of milk to water in the resulting mixture?
1. A.1 : 1
2. B.2 : 3
3. C.3 : 2
4. D.5 : 5
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Answer: A
Q632025 · 18 Sept 2025 · Shift 3
A solid right circular cone is divided by a plane parallel to its base into a smaller cone and a frustum. If the volume of the frustum is 7 times the volume of the smaller cone, what is the ratio of the heights of the frustum and the smaller cone?
1. A.1 : 1
2. B.2 : 1
3. C.3 : 1
4. D.4 : 1
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Answer: A
Q702025 · 18 Sept 2025 · Shift 3
The radii of two circles are in the ratio 1 : 2. If the length of a direct common tangent is 8 cm and the distance between their centres is 10 cm, find the radius of the smaller circle.
1. A.2 cm
2. B.4 cm
3. C.5 cm
4. D.6 cm
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Answer: D
Q522025 · 17 Sept 2025 · Shift 1
Given that , find the compound ratio .
1. A.20 : 24 : 56 : 63
2. B.5 : 6 : 7 : 9
3. C.5 : 6 : 14 : 9
4. D.20 : 24 : 42 : 63
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Answer: A
Q672025 · 17 Sept 2025 · Shift 1
A sector of a circle has a central angle of $6 0^{\circ}$ and a radius of 8 cm. Another sector of the same circle has a central angle of $\frac{π}{3}$ radians. What is the ratio of the area of the first sector to the area of the second sector?
1. A.2 : 3
2. B.1 : 2
3. C.1 : 1
4. D.1 : 3
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Answer: C
Q602025 · 17 Sept 2025 · Shift 2
A barrel contains a mixture of alcohol and water in the ratio 7 : 4 respectively. If 12 litres of water are added to it, the ratio of alcohol to water becomes 7 : 6. Find the initial total quantity of the mixture in the barrel.
1. A.33 litres
2. B.44 litres
3. C.55 litres
4. D.66 litres
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Answer: D
Q642025 · 17 Sept 2025 · Shift 2
A hollow hemisphere has uniform thickness. Its inner radius is r, and outer radius is R. If R = 2r, find the ratio of outer to inner curved surface areas.
1. A.4 : 1
2. B.7 : 4
3. C.6 : 5
4. D.2 : 5
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Answer: A
Q672025 · 17 Sept 2025 · Shift 2
In an equilateral triangle with side length 'a', what is the ratio of the circumradius to the inradius?
1. A.2 : 1
2. B.3 : 1
3. C.4 : 1
4. D.1 : 2
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Answer: A
Q692025 · 17 Sept 2025 · Shift 2
In a trapezoid ABCD with AB parallel to CD, the diagonals AC and BD intersect at E. What is the ratio of the area of △ABE to the area of △CDE?
1. A.The ratio of AB to CD squared.
2. B.The ratio of AB to CD.
3. C.The ratio of the perimeter of △ABE to the perimeter of △CDE.
4. D.The ratio of the area of △ABC to the area of △BCD.
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Answer: A
Q602025 · 17 Sept 2025 · Shift 3
A cone and a sphere have equal volumes. If the cone's height is twice its radius, what is the ratio of the cone's radius to the sphere's radius?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: A
Q612025 · 17 Sept 2025 · Shift 3
A hemisphere and cylinder of equal radii have equal total surface areas. Find the ratio of cylinder height to radius.
1. A.1:2
2. B.7:4
3. C.6:5
4. D.2:5
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Answer: A
Q672025 · 17 Sept 2025 · Shift 3
A sector has a central angle of $18 0^{\circ}$ and a radius of 12 cm. Another sector has a central angle of $π /2$ radians and the same radius. What is the ratio of the area of the first sector to the area of the second sector?
1. A.1:2
2. B.2:1
3. C.3:1
4. D.1:3
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Answer: B
Q702025 · 17 Sept 2025 · Shift 3
The ratios of the perimeters of two similar triangles are expressed as 3 : 5. Together, their areas total 34 cm². What is the area of the larger triangle?
1. A.9 cm²
2. B.15 cm²
3. C.25 cm²
4. D.35 cm²
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Answer: C
Q632025 · 16 Sept 2025 · Shift 2
The ratio of the speeds of a car and a bus is 3 : 4. If the bus covers a distance of 320 km in 4 hours, what is the speed of the car (in km/h)?
1. A.60 km/h
2. B.75 km/h
3. C.80 km/h
4. D.90 km/h
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Answer: A
Q682025 · 16 Sept 2025 · Shift 2
A circular fountain with a radius of 7 m is encircled by a grass bed that is 3.5 m wide. Determine the ratio of the area of the grass bed to the area of the fountain.
1. A.3 : 2
2. B.2 : 1
3. C.5 : 4
4. D.4 : 1
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Answer: C
Q532025 · 16 Sept 2025 · Shift 3
What should be subtracted from 7, 9, 8, 11 so that the remaining numbers may be proportional?
1. A.12
2. B.5
3. C.1
4. D.6
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Answer: B
Q622025 · 16 Sept 2025 · Shift 3
A 90-litre mixture contains milk and water in the ratio 7 : 2. If 'x' litres of milk and 'x' litres of water are added to the mixture, the new ratio of milk to water becomes 5 : 2. What is the value of 'x'?
1. A.13.33 litres
2. B.10.54 litres
3. C.15 litres
4. D.20 litres
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Answer: A
Q672025 · 16 Sept 2025 · Shift 3
The ratio of the radii of two car tyres is . If the area of the smaller tyre is 100 cm², what is the area of the larger tyre?
1. A.200 cm²
2. B.300 cm²
3. C.400 cm²
4. D.500 cm²
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Answer: A
Q702025 · 16 Sept 2025 · Shift 3
In triangle ABC, a line segment DE is drawn through the centroid G, parallel to side BC. D lies on AB and E lies on AC. What is the ratio of the area of the smaller triangle ADE to the area of the trapezoid DECB?
1. A.1 : 1
2. B.1 : 2
3. C.4 : 5
4. D.4 : 9
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Answer: C
Q512025 · 15 Sept 2025 · Shift 1
If A : B = 7 : 5, B : C = 2 : 3, and C : D = 4 : 5, find the ratio A : D.
1. A.14 : 25
2. B.28 : 25
3. C.56 : 75
4. D.75 : 56
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Answer: C
Q552025 · 15 Sept 2025 · Shift 1
A container holds a mixture of three liquids A, B, and C in ratio 2 : 3 : 5. If 6 litres of liquid A, 12 litres of liquid B, and a certain amount of liquid C are added to the container, the new ratio of liquids A, B, and C becomes 3 : 5 : 8. Find the quantity (in litres) of liquid C added.
1. A.15 litres
2. B.16 litres
3. C.18 litres
4. D.20 litres
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Answer: C
Q632025 · 15 Sept 2025 · Shift 1
A cistern contains 100 litres of pure syrup. 10 litres of syrup are drawn out and replaced by water. Then, 10 litres of the mixture are drawn out and replaced by water again. What is the ratio of syrup to water in the final mixture?
1. A.18 : 1
2. B.89 : 14
3. C.81 : 19
4. D.18 : 17
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Answer: C