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In a school, ratio of boy students and girl students is 5 : 2. If the number of boy students is 450 more than the girl students, how many students are there in the school ?
Let the number of boy students in the school be 5x and that of girlstudents is 2x.
Then, 5x – 2x = 450 ⇒ x = 150
∴ Number of total students = 5x + 2x = 7 × 150 = 1050
B F J : R : : O A F : ?
⇒ (2 + 6 + 10) : 18 : : (15 + 1 + 6) : ?
X P T : J H L : : B D L : ?
⇒ (24 + 16 + 20) : (10 + 8 + 12) : : (2 + 4 + 12) : ?
If 40% of 3/4 of 4/5 of some number is 48, what would be the value of 1 per cent of that number ?
Let the number be = x
∴ 1 per cent of the number
Expression = 2^{(–2)2} =
2(–2) × (–2) =
2^{4} = 16
Square of the sum of two positive numbers is 9. What would be the value of the sum of the cubes of these numbers ?
(Sum of two positive numbers)^{2} = 9 = 3^{2 }
⇒ Sum of two positive numbers = 3 = (1 + 2)
∴ Sum of the cube of those numbers
= 1^{3} + 2^{3} = 1 + 8 = 9
Which of the following diseases is caused by virus ?
Chromatographic technique is used for the following purposes—
At simple interest, a principal becomes double in 16 years. How much will the principal become in 8 years ?
Let the sum of money = Rs. P
It becomes double in 16 years. Let the rate of simple annual interest be R%
A trader allows 10% discount on marked price of an article and gets 20% profit. If the marked price of the article is Rs. 50, what is its cost price ?
Let the cost price of the article be = Rs. x
Then, the sale price of the article
Marked price of the article = Rs. 50 As per question
Find the least number which when divided by 4, 12 and 16 leaves remainder 3 in each case, but it is perfectly divisible by 7.
L. C. M. of 4, 12, 16 = 48
∴ 48 × 1 + 3 = 51, Not divisible by 7
and 48 × 2 + 3 = 99,
Not divisible by 7 but, 48 × 3 + 3 = 147, Divisible 7
∴ Lowest multiple of 7 = 147
At what rate of simple interest, will a sum of money become 4 times in 15 years ?
Let simple annual interest be
= R% Then, as per question
A train 130 metres, running at a speed of 45 km/hr, crosses a bridge in 30 seconds. What is the length of the bridge ?
Let the length of the bridge be = x metre Speed of the train = 45 km/hr
Distance = Speed × time
x = 375 – 130
= 245 metres
Square of the sum of two positive numbers is 9. What would be the value of the sum of the cubes of these numbers ?
(Sum of two positive numbers)^{2} = 9 = 3^{2 }
⇒ Sum of two positive numbers = 3 = (1 + 2)
∴ Sum of the cube of those numbers
= 1^{3} + 2^{3} = 1 + 8 = 9
4/5 part of a canister is filled with oil. 6 bottles of oil is taken out of it, leaving the threefourth part of the canister filled with oil. How many bottles of oil can fill the entire canister ?
Let the capacity of the canister be = x bottles
Then, as per question
x = 6 × 20 = 120 bottles
If x : y : : 5 : 2 then the value of 8x + 9y : 8x : 2y will be—
x : y : : 5 : 2
A fraction has the same ratio with 1/27, that 3/11 has with 5/9 . What is that fraction ?
Let required fraction be = x/1
Then, as per question,
12 is the H. C. F. of three numbers. If the ratio of these numbers is 1 : 2 : 3, then what are these numbers ?
Let three required numbers be x, 2x and 3x, respectively. H. C. F. of three numbers = x =12
∴ Required numbers = 12, 12 × 2, 12 × 3 = 12, 24, 36
Average of first 50 natural numbers
There is a group of 8 men. If a new man replaces a man of this group of 65 kg, average weight of the group rises by 1·5 kg. What is the weight of this new men ?
Weight of new man = 65 kg. + 8 × 1·5
= (65 + 12) kg. = 77 kg.
Average of 11 observations is 60. 58 is the average of first 5 observations and 56 is the average of last five observations. What is the 6th observation ?
6th observation = 11 × 60 – [5 × 58 + 5 × 56]
= 660 – [290 + 280]
= 660 – 570 = 90
Average age of 25 students is 10 years. Average age rises by one year, if the age of the teacher is also included. What is the age of the teacher ?
Teacher’s age
= (25 + 1) × (10 + 1) – 25 × 10
= 286 – 250
= 36 years
Sum of three numbers is 98. Ratio of first and second numbers is 2 : 3 and that of second and third is 5 : 8. What is second number ?
Let the three numbers be A, B and C respectively.
∴ A : B = 2 : 3 = 10 : 15 B : C = 5 : 8 = 15 : 24
∴ A : B : C = 10 : 15 : 24
As per question
10x + 15x + 24x = 98
x = 98/49 = 2
Second number = B = 15x = 15 × 2 = 30
How many are the numbers between 200 and 600 which are perfectly divisible by 4, 5 and 6 ?
L. C. M. of 4, 5 and 6 = 2 × 2 × 3 × 5 = 60
∴ The number of required numbers
[240, 300, 360, 420, 480 and 540]
Area of the largest triangle drawn in a semicircle of radius r will be—
Perpendicular height of the largest triangle drawn in a semicircle of radius r = r
What would be the value of log 9, if log 27 = 1·431 ?
log 27 = log 3^{3}
= 3·log 3 = 1·431
Three cubes of iron of sides 6 cms., 8 cm and 10 cm are melted and then converted into a single big cube what would be the side of this new cube ?
Let x be a side of newly formed cube after melting the three cubes.
x^{3} = (6^{3} + 8^{3 }+ 10^{3}) cm^{3}
= (216 + 512+ 1000) cm^{3}
= 1728 cm^{3}
= 123 cm^{3}
∴ x = 12 cm
If each side of a square is extended by 25% its area will increase by—
Let the side of a square be = a
Length of the side after elongating 25%
∴ Percentage increase in area of the square
At simple interest, if a sum of money becomes double in 6 years, after how long will it become 4 times ?
Let any sum be = Rs. P
It becomes double in 6 years at the annual simple interest rate of R%
Let that sum become 4 times in T years
If cost price of 12 tables is equal to the sale price of 16 tables. What is the percentage of loss ?
Cost price of 12 tables = Sale price of 16 tables
If an electric press is sold for Rs. 600, a profit of 20% is obtained. What would be its cost price, if it is sold at a profit of 15% ?
Let the cost price of electric press be = Rs. x
As per question,
∴ First sale price of the press
If 75% of some number is added to 75, the same original number is obtained. What is this number ?
Let the required number be = x
Then, 75 + 75% of x = x
x = 4 × 75 = 300
A is 10% taller than B. How much B is shorter than A ?
Let the height of B be = 100 cm
∴ Fall of percentage in required height
65xy is a number of 4 digits in which x and y are such two digits that 65xy is perfectly divisible by 80. Then x + y will be equal to—
As per question, in the number 65 xy, x and y are such digits that 65 x y is fully divisible by 80.
Then, y = 0
In the numbers 651, 652, 653, 654, … 659, only 656 is divisible by 8.
Namely, 6560 ÷ 80 = 82
So, x = 6
∴ x + y = 6 + 0 = 6
A can do a piece of work in 6 days and B in 12 days. If both work together and complete the piece of work, what part of the work will be done by A ?
Part of work done by (A + B) in 1 day
⇒ (A + B) will complete the work in = 4 days
∴ Part of work done by A in 4 days = 4 × 1/6 = 2/3 par
The sum of first 8 terms of a Geometric Progression is 6560 and common ratio is 3. The first term will be—
First term of geometric progression = a
If a monthly increment of 2 2/3 % is allowed to an employee, he gets Rs. 72 more. His monthly income will be—
Let monthly income of the employee be = Rs. x
x = 9 × 300 = Rs. 2700
Angles of a triangle are in the ratio 2 : 7 : 11. Meaurements of the angle will be—
Let the values of angles of a triangle be 2x°, 7x° and 11x°, respectively
2x° + 7x° + 11x° = 180°
⇒ 20x° = 180°
∴ x° = 9°
Hence, the values of the angles of triangle are 18°, 63°, 99°.
Ratio of milk and water is 7 : 3 in a mixture of 30 litre. How much water should be added to the mixture to make the ratio 3 : 7 ?
Volume of milk in the mixture
Volume of water in the mixture
For required ratio in the mixture, let the volume of mixed water be = x litre Then,
Radius of a circumcircle of an equlilateral triangle is 8 cm. What would be the radius of the incircle of this triangle ?
Let the one side of the equilateral triangle be = a cm
Then length of radius of circumcircle
Length of the radius of circumcircle
Missing term in the series
0, 3, 8, 15, 24, …, 48 is—
Formation process and sequence of series are as below—
Missing term = 24 + 11 = 35
Rationalisation factor of 3⎯√3 = ⎯√3
[ 3√⎯ 3 × ⎯√3 = 9]
The atom which has comparatively less number of electrons is called—
10 identical taps can jointly fill a tank in 24 minutes. How long will nine of these taps take to fill this tank jointly ?
Part of the tank filled in 1 minute by 10 taps = 1/24
⇒ Part of the tank filled by one tap in 1 minute = 1/240
∴ Part of the tank filled by 9 taps in 1 minute = 9/240
Time taken by 9 taps to fill the tank fully = 240/9
= 26 2/3 minutes
During Alexandar’s invasion, which river was the eastern border of India ?
There is a cylindrical electric geyser with height 1·5 m and diameter 35 cm. Ignoring the thickness of its well, calculate its external lateral surface area.
Area of the external lateral surface of the geyser = 2π R. H.
A discount of 16% is allowed on marked price of an article. If its sale price is Rs. 546, what would be its marked price ?
Let marked price of the article be = Rs. x Then, as per question,
Viscosity of which of the following is maximum—
This time Ritu’s age is four times to that of her brother Raj’s age. After 4 years, her age will be twice the age of Raj. What is present age of each of them ?
Let present age of Ritu be 4x years and that of Raj is x years. Then
∴ Present age of Ritu is 8 years and that of Raj is 2 years.
After dissolution of Lok Sabha, when is the post of Speaker abolished ?
The most appropriate metal for permanent magnet is—
As the molecular weight of a liquid rises, its viscosity—
Why does a soap bubble appear colourful in sunlight ?
Which of the following states is the foremost rubber producer ?
Who presides over the joint session of both the Houses of Parliament ?
Under which Constitution Amendment have the fundamental duties of Indian citizens been included in the constitution ?
Who was the chief guest at the celebration of India’s Republic Day 2008 ?
Radius of the base of a cylinder is 3 metre and its height is 14 m. Curved surface of the cylinder will be—
Curved surface = 2πrh
= 2 x 22/7 x 3 x 14 = 264 m^{2}
Second Karnataka War (1760) was fought between—
0·1 × 0·1 × 0·01 × 0·1 = 0·00001
Find the total surface area of a solid cylinder of radius 5 cm and height 10 cm. Give the answer in π.
Area of whole curved surface of the cylinder = 2πR (H + R)
= 2π × 5 × (10 + 5) = 150 π cm^{2}
Four men working together take 3 hours to paint a wall. How much time would six men take to do the same job ?
4 Men complete the work in = 3 hours
⇒ 1 man will comlete the work in = 4 × 3 hrs.
∴ 6 men will complete the work = 4x3/6 = 2 hr
A man goes 18 km down the stream in 4 hours and returns against the stream in 12 hours. The speed of the stream in km/hr is—
Speed of current = 1/2 [Speed in direction of current – Speed in anticurrent direction]
50 g of an alloy of gold and silver contains 80% gold (by weight). The quantity of gold, that is to be mixed up with this alloy, so that it may contain 95% gold, is—
Quantity of gold in the alloy = = 50 × 80/100 = 40 gms.
Let the quantity of gold mixed with be = x gm
Then, as per question,
⇒ 800 + 20x = 950 + 19x
⇒ (20 – 19)x = 950 – 800
∴ x = 150 gm
If a bucket is 80% full, then it contains 2 litre more water than when it is 66 2/3 % full. What is the capacity of the bucket ?
Let the capacity of the bucket be = x litre
Then, as per question,
The monthly income of a person was Rs. 13500 and his monthly expenditure was Rs. 9000. Next year his income increases by 14% and his expenditure by 7%. Then the percentage increase in his savings is—
Monthly income = Rs. 13,500
Monthly expenditure = Rs. 9000
⇒ Monthly savings = 13500 – 9000 = Rs. 4500
As per question next year
Monthly income = 13500 × 114 /100 = Rs. 15390
Monthly income = 9000 × 107/100 = Rs. 9630
∴ Monthly savings = 15390 – 9630 = Rs. 5760
∴ Percentage of required in savings
= (5760 – 4500)/4500 × 100% = 28%
A ladder 13 feet long stands upright against a wall. How far must the bottom of the ladder be pulled out so as to lower the top by a foot ?
Let bottom B of the ladder be pulled out be x feet from the wall so that the top A is lowered by 1 foot.
BQ^{2 }= AB^{2} – AQ^{2 }
⇒ x^{2} = 13^{2} – 12^{2}
= 169 – 144 = 52
∴ x = 5 feet
Given that √3 = 1·73, the value of correct to three places of decimal, is—
Liquidregulated brakes in automobiles function on—
A girl is sitting in a swing and swinging. Suddenly, she stands up, then time priod will—
Which of the following is the function of carburettor ?
Alloy of which metals is used to make the parts of aircrafts and railway wagons.
In which of the following media isthe velocity of sound maximum ?
How does the escape velocity of a matter depend on its mass m ? It is directly proportional to—
A body is in simple harmonic motion. Its potential energy will remain in which position ?
Which of the following is the heaviest metal ?
Which of the following converts solar energy directly into electrical energy ?
Which of the following is called Land of Morning Calm ?
Where is the headquarter of F. A. O. located ?
Which of the following cathode materials offers the highest emission capacity ?
Main function of moderator in nuclear reactors is—
Dimensions of ‘a’ in the vander Waal’s equation ( p + a/v^{2} ) .(v – b) = RT are
Dimension of P and a/√2 will be the same
In the first week of the month, owner of a factory manufactured 40% of its quota. In the second week, he manufactured 50% of the first week’s production. During the third and fourth weeks, he manufactured 17488 tools. What is its monthly quota ?
Let number of tools manufactured monthly in the factory be = x
Then, a per question, Production in first week = 40% of x
Production in second week
∴ Production in third and fourth weeks
At a profit of 12%, ‘A’ sells a camera to ‘B’. At a loss of 9%, ‘B’ sells it to ‘C’. If ‘C’ purchased it for Rs. 1896, what was the cost price for ‘A’ ?
Let cost price of camera for A be = Rs. x ⇒ Cost price of the camera for B
⇒ Cost price of camera for C
Given expression = 0·1 × 0·1 × 0·001 × 0·1 = 0·000001
JKLM is a kite and its diagonals intersect at 0. If LKLM = 2 LKJM and LKJM = 68°, find out the value of LLKO—
∠ KLM = 2 × ∠ KJM = 2 × 68° = 136°
Radioactive iodine is used in the treatment of the diseases of which of the following ?
Which of the following will decompose if electric current passes through its aqueous solution ?
If current passes through a coil, the energy accumulates in the following form—
Find out the missing term in the following series—
3, 4, 10, ?, 136, 685
Following is the given number series—
In some code language, OTRN is written as MRPL. How can EJID be written in the same language ?
A cricketer has some average of runs of his 16 innings. He scored 85 runs in his 17th innings. Then his average increased by 3 runs. What is average of runs after 17th innings ?
Rise in average after 17th innings = 3
Total increase in runs after 17th innings = 3 × 17 = 51
The player scored 85 runs in 17th innings.
∴ His averaged of 16th innings = 85 – 51 = 34
∴ Average of his 17th innings = 34 + 3 = 37
What is the percentage of pure gold in 18 carat ?
18 Percentage of pure gold in 18 carat = 18/24 × 100%
= 3/4 × 100% = 75%
Under which constitution amendment has the age limit for voting been changed from 21 years to 18 years ?
Among the following planets of solar system, which is the largest ?
Which of the following glands is called master gland in human body ?
Which metal is used in storage battery (accumulator) ?
If log_{10} (x^{2 }– 6x + 45) = 2, then the value of x will be—
log10 (x^{2} – 6x + 45) = 2
⇒ x^{2} – 6x + 45 = 10^{2} = 100
⇒ x^{2} – 6x – 55 = 0
⇒ (x – 11) (x + 5) = 0
∴ x = 11, – 5
Velocity of a particle is reduced to onethird of its initial velocity. Kinetic energy of the particle will become—
Bauxite is an ore of which of the following metals—
From the top of a building, a ball is dropped with an acceleration of 9·8 m/s^{2}. After 3 seconds, its velocity will be—
Let required velocity be = V m/sec
V = U + ft
⇒ V = 0 + 9·8 × 3
∴ V = 29·4 m/sec^{2}
Ratio of the magnetic fields of a magnet at end on distance d from the magnet and at broadsideon position will be—
What would be the temperature of the watersurface of a lake which is just going to freeze ?
A jet engine functions on which of the following principles ?
A wire of 4 Ω resistance is folded in the middle at 180° and its both the ends are joined. What will be its new resistance ?
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