Find real questions from previous competitive exam papers with answers and solutions.
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?
196
630
1260
2520
Correct answer
630
Why this answer is correct
Given:
Numbers = 12, 18, 21 and 30.
Calculation:
the least number which when doubled will be exactly divisible by 12, 18, 21 and 30.
LCM of (12, 18, 21, 30) = 1260.
∴ Required answer will be half of LCM = 1260/2 = 630.
Successive discount of 15% and 35% is equivalent to a single discount of:
42.28%
12.5%
44.75%
33.33%
Correct answer
44.75%
Why this answer is correct
Given:
Successive discounts of 15% and 35%
Calculation:
⇒ Equivalent discount = 1 - (1 - 15/100) × (1 - 35/100) = 0.4475 or 44.75%
Therefore, successive discounts of 15% and 35% is equivalent to a single discount of 0.4475 or 44.75%.
The halves of the diagonals of a rhombus are 75 cm and 90 cm. Find its area.
6750 cm2
27000 cm2
3375 cm2
13500 cm2
Correct answer
13500 cm2
Why this answer is correct
Shortcut Trick
Area of a rhombus = 2 × (Product of its half-diagonals).
Given half-diagonals are 75 cm and 90 cm.
Area = 2 × 75 × 90
Area = 150 × 90 = 13500 cm2.
∴ The correct answer is 13500 cm2.
Alternate Method
Given:
Half of first diagonal (d1/2) = 75 cm
Half of second diagonal (d2/2) = 90 cm
Formula Used:
Area of Rhombus = (1/2) × d1 × d2
⇒ First diagonal (d1) = 2 × 75 = 150 cm
⇒ Second diagonal (d2) = 2 × 90 = 180 cm
⇒ Area = (1/2) × 150 × 180
⇒ Area = 150 × 90
⇒ Area = 13500 cm2
∴ The correct answer is 13500 cm2.
Additional Information
Diagonal Property
The diagonals of a rhombus bisect each other at right angles (90°).
Side Length Formula
The side (a) of a rhombus can be calculated using half-diagonals: a = √((d1/2)2 + (d2/2)2).
Perimeter of Rhombus
The perimeter is 4 × side length, as all four sides of a rhombus are equal.
Directions
What approximate value will come in place of the question mark (?) in the following question?
15.5% of 850 + 24.8% of 650 = ?
293
385
210
375
Correct answer
293
Why this answer is correct
Given:
15.5% of 850 + 24.8% of 650 = ?
Calculation:
Let the unknown number be x.
15.5% of 850 + 24.8% of 650 = x
⇒ × 850 + × 650 = x
⇒ 131.75 + 161.2 = x
⇒ x = 292.95 ≈ 293
∴ 15.5% of 850 + 24.8% of 650 ≈ 293
A certain number is subtracted from each of the numbers 20, 24, and 29. After the subtraction, the resulting numbers are in proportion. What is the number that was subtracted?
6
4
5
3
Correct answer
4
Why this answer is correct
Shortcut Trick
The fastest way to solve this is by testing the options to find a common ratio.
Let's check Option 2, which gives the value 4.
Subtracting 4 from 20, 24, and 29 gives the numbers 16, 20, and 25.
Three numbers are in continued proportion if the ratio of the first to second equals the second to third.
Checking the ratios: 16 ÷ 20 = 4/5 and 20 ÷ 25 = 4/5. The condition is perfectly satisfied.
∴ The correct answer is 4.
Alternate Method
Given:
Three numbers: 20, 24, and 29
Formula Used:
If three numbers a, b, and c are in continued proportion, then a/b = b/c or b2 = a × c.
Calculations:
Let the number subtracted from each value be x.
⇒ The new numbers become (20 − x), (24 − x), and (29 − x).
⇒ According to the continued proportion rule: (20 − x) ÷ (24 − x) = (24 − x) ÷ (29 − x)
⇒ Cross-multiplying, we get:
⇒ (20 − x) × (29 − x) = (24 − x)2
⇒ 580 − 20x − 29x + x2 = 576 − 48x + x2
⇒ 580 − 49x = 576 − 48x
⇒ 580 − 576 = 49x − 48x
⇒ x = 4
∴ The correct answer is 4.
Additional Information
Proportion
Four numbers a, b, c, and d are said to be in proportion if a ÷ b = c ÷ d, denoted as a:b :: c:d.
Continued Proportion
Three numbers a, b, and c are in continued proportion if a:b = b:c, meaning b2 = a × c. Here, b is called the mean proportional between a and c.
Componendo and Dividendo Rule
For any valid proportion a/b = c/d, the rule states that (a + b) ÷ (a − b) = (c + d) ÷ (c − d). This property is highly useful for rapidly simplifying complex fractional equations without cross-multiplying.
A dealer marks his goods at 44% above the cost price. Then he allows 50% discount on it. What would be his loss percentage?
25%
28%
26%
32%
Correct answer
28%
Why this answer is correct
Given
Mark-up rate = 44%
Discount = 50%
Formula used:
M.P = (100 + m)/100 × C.P
where, m = mark-up rate, M.P = marked price and C.P = cost price
S.P = (100 - d)/100 × M.P
where, d = discount, M.P = marked price and S.P = selling price
Loss% = (C.P - S.P)/C.P × 100
Calculation
Let the C.P. be 100.
M.P = (100 + 44)/100 × 100
M.P = 144/100 × 100
M.P = 144
Now, the S.P will be:
S.P = (100 - 50)/100 × 144
S.P = 50/100 × 144
S.P = 72
Loss% = (100 - 72)/100 × 100
Loss% = 28
∴ The correct answer is option 2.
The value of (1 + (1 - 2)-1 + 2 - (1 - 2)-2)2 is:
1
2
0
-1
Correct answer
1
Why this answer is correct
Given:
(1 + (1 - 2)-1 + 2 - (1 - 2)-2)^2
Calculations:
(1 + (1 - 2)-1 + 2 - (1 - 2)-2)2
(1 - 2) is -1, so (1 - 2)-1 is -1 and (1 - 2)-2 is 1
⇒ (1 - 1 + 2 - 1)2
⇒ (1)2 = 1
∴ The value of the given expression is 1.
If 2P = 3Q = 5R and P + Q + R = 6200, then the difference between P and R is:
3000
2000
1200
1800
Correct answer
1800
Why this answer is correct
Given:
2P = 3Q = 5R
P + Q + R = 6200
Concept or Formula:
Use the given equations to express P, Q, and R in terms of a common variable.
Substitute these expressions into the second given equation to solve for the common variable.
Then calculate the values of P and R using the common variable.
The difference between P and R can be found by subtracting the smaller value from the larger one.
Solution:
Let 2P = 3Q = 5R = k (some constant)
⇒ P = k/2, Q = k/3, and R = k/5
Substitute P, Q, R in P + Q + R = 6200
⇒ k/2 + k/3 + k/5 = 6200
Solve the above equation for k,
⇒ k (1/2 + 1/3 + 1/5) = 6200
⇒ k (15/30 + 10/30 + 6/30) = 6200
⇒ k × 31/30 = 6200
⇒ k = 6200 × 30/31
⇒ k = 6000
Substitute k = 6000 in P = k/2 and R = k/5
⇒ P = 6000/2 = 3000 and R = 6000/5 = 1200
Find the difference between P and R
⇒ P - R = 3000 - 1200 = 1800
Therefore, the difference between P and R is 1800.
A hemispherical dome of a tomb having diameter of 3.5 m is to be painted. If the cost of painting is 20 paise per cm2, then what is the cost (in Rs.) of painting the dome from inside? Take π =
Rs. 38,500
Rs. 35,000
Rs. 28,500
Rs. 25,000
Correct answer
Rs. 38,500
Why this answer is correct
Shortcut Trick
Radius (r) = 3.5 m / 2 = 1.75 m = 175 cm.
Inner Surface Area of dome = 2 × π × r2.
Area = 2 × (22/7) × 175 × 175 = 1,92,500 cm2.
Total Cost = Area × Rate = 1,92,500 × 0.20 = ₹38,500.
∴ The correct answer is ₹38,500.
Alternate Method
Given:
Diameter of the hemispherical dome (d) = 3.5 m
Cost of painting = 20 paise per cm2
Formula Used:
Inner surface area of a hemisphere = 2πr2
Total Cost = Surface Area × Rate
⇒ Radius (r) = d / 2 = 3.5 / 2 = 1.75 m
⇒ Radius in cm = 1.75 × 100 = 175 cm
⇒ Inner Surface Area = 2 × (22/7) × 175 × 175
⇒ Inner Surface Area = 2 × 22 × 25 × 175 = 1,92,500 cm2
⇒ Rate of painting = 20 paise = 20/100 = ₹0.20 per cm2
⇒ Total Cost = 1,92,500 × 0.20
⇒ Total Cost = ₹38,500
∴ The correct answer is ₹38,500.
Additional Information
Surface Area of a Sphere
The total surface area of a complete sphere is given by 4πr2, which is exactly double that of the curved surface area of a hemisphere.
Total Surface Area of a Hemisphere
If the base of the hemisphere is also included (closed hemisphere), the total surface area is 3πr2 (Curved area + Base area).
Volume of a Hemisphere
The volume of a hemisphere is half the volume of a sphere, calculated as V = (2/3)πr3.
Cost Calculation Rule
Always ensure that the units of dimensions (cm, m) and the rate (per cm2, per m2) are consistent before performing the final multiplication.
The pie chart given below shows the production of wheat by six states. The total production of wheat by all these six states is 3600. The production of wheat of a particular state is shown in terms of degree with respect to the total production of wheat by all these six states.
What is the difference between average production of wheat by P and Q and the average production of wheat by R and T?
300
500
400
200
Correct answer
400
Why this answer is correct
Calculation:
Total production of wheat by 6 states = 360° = 3600
⇒ 1° = 10
Production of state P = 110° = 110 × 10 = 1100
Production of state Q = 70° = 70 × 10 = 700
Average production by state P & Q = (1100 + 700)/2 = 900
Production of state R = 80° = 80 × 10 = 800
Production of state T = 20° = 20 × 10 = 200
Average production by state R & T = (800 + 200)/2 = 500
Difference between the average production of P and Q and R & T = 900 - 500 = 400
∴ The correct answer is 400.