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Three taps A, B, and C can fill a tank in 20, 24, and 30 hours respectively. How long (in hours) would the three taps take to fill the tank if all of them are opened together?
B can fill 1 unit of water in the tank in 1/24 hours
C can fill 1 unit of water in tank in 1/30 hours
(A+B+C) can fill 1 unit of water in tank in 1/20+1/24+1/30=6+5+4/120 =15/120=18 days
Therefore,
(A+B+C) can fill a full tank in 8 days.
If the rate of interest is 8% per annum and Rs. 10000 lent at the compound interest half yearly then calculate the equivalent simple rate of interest for the first year?
the rate of interest is 8% per annum lent at the compound interest half yearly.
Compound interest for 6 months = 4%
Compound interest next 6 months = 4%+4of 4%=(4+.16)%=4.16%
the equivalent simple rate of interest for the first year=4+4.16=8.16%
PAB and PCD are two secants to a circle. if PA =10cm , AB =12cm and PC =11cm, then what is the value of PD?
The speed of a boat in still water is 10 km/hr. It covers a distance of 50 km upstream in 6 hours. What is the speed (in km/hr) of the stream?
500 litres of milk solution has 40% milk in it. How much more milk should be added to make it 60% in the solution?
Water is 60% of 500 = 300 litres
ATQ,
40%of mixture=water=300 litres
New mixture quantity=300/40% =7 50 liters
The quantity of milk in the mixture= 60 % of 750=450 liters
Required milk to be mixed=450-200=250 liters
Therefore,
250 liter of milk should be added to make it 60% in the solution.
The shadow of a tower on ground level is increased by 20 m, when the angle of depression by the sun changes from 60∘ to 30∘ . The height of the tower is?
Let the height of tower DC = h meter tan60∘=h/BC
Putting the value of BC from equation(1) in equation (2), we get
∴ h=10√3 meter
What will be the sum of all odd whole numbers between 10 and 38?
That is,
Last term = First term + (number of terms-1) × Common difference
ATQ,
37 = 11 + (N-1) × 2
So, N or Number of terms =14
Now,
Sum of terms = N/2 [2×first term(N−1)×d]
ATQ,
Sum = 14/2 [2×11+(14−1)×2]
Sum = 336
Therefore,
The Sum of all odd whole numbers between 10 and 38 is 336
If the volume of two cubes is in the ratio 125 : 1, then what is the ratio of their edges?
A ,B and C invest in a business in the ratio 3:6:5. A and C are working partners.Only B is a sleeping partner hence his share will be 3/4th of what it would have been if he were a working partner. If they make Rs. 50000 profit, half of which is reinvested in the business and the other half is distributed between partners, then how much does C get (in Rs )?
old ratio
A:B:C
3: 6: 5
ATQ. B′ s share =6×(3/4)=9/2
new ratio 3:9/2:5
6: 9: 10
total profit =50000 after reinvestment the profit =50000/2=25000
C's share = (25000x10)/25 = Rs. 10000
The HCF and LCM of two numbers are 45 and 270 respectively. If the ratio of the two numbers is 2:3 and smaller of the two numbers is X, then find X2
Product of numbers =product of lcm and hcf
2y×3y=45×270
y2 = 45×45
y=45
then smaller no. X=2×45=90
X2 = (90)2=8100
In how many years will Rs 2,000 yield Rs 662 as compound interest at 10% per annum compounded annually?
n = 3 years
What is the value of tan (π/4 + A) × tan (3π/4 + A)?
The distance between the centers of the two circles is 61cm and their radius is 35cm and 24cm. What is the length(in cm) of the direct common tangent to the circles?
Standard deviation
Standard deviation =
If a dairy mixes cow’s milk which contains 10%fat with buffalo’s milk which contains 20% fat,then the resulting mixture has the fat of 120/7% . In what ratio was the cow’s milk mixed with buffalo’s milk?
ratio 2:5
If two complimentary angles are in the ratio of 4:5, find the greater angle.
4x+5x=90∘
9x=90∘
x=10∘
Greater angle = 5x=50∘
In the given figure, in a right angle triangle ABC, AB=12 cm and AC =15cm. A square is inscribed in the triangle. One of the vertices of the square coincides with the vertex of the triangle. What is the maximum possible area of the square ( cm2 )?
then, BC=152−122=9cm
side of square =(P×B)/(P+B) where, Pe perpendicular, B = base side of the square =(12×9)/21=36/7
area of the largest square that can be formed inside the triangle = (36/7)2 = (1296/49)y
What is the measure of the two equal angles of a right isosceles triangle?
A.T.Q ∠B=90∘
and AB=BC
So, ∠A=∠C
we know that ∠A+∠B+∠C=180∘
x+90∘+x=180∘
2x=90∘
X = 450
If 1082 =11664 , then what is the value of √1.1664 + √116.64 ?
The length and breadth of a rectangular field are in the ratio of 5 : 2. If the perimeter of the field is 140 metres, then what is the breadth (in metres)?
Perimeter=2(Length + Breadth)
140=2(5x+2x)
70=7x
So, x=10 m
Therefore, Breadth of rectangle = 2×10=20 metre
Calculate the amount on Rs. 37,500 @ 8% p.a compounded half yearly for 1 1/2 years.
amount =P(1+(R/100))n
The mean of 17 numbers is 12. If two numbers 9 and 15 are removed, then what will be the mean of the remaining number?
After removal of 9 and 15, the the sum becomes 180.
Therefore,
Mean of remaining 15 numbers = 180/15=12
Ram Naresh got two successive discounts, a bag with a list price of Rs. 400 is available at Rs. 160. If the second discount is 20%, find the first discount.
First a discount of 20% means that you multiply the price by .80(1−0.20) The initial price is therefore first multiplied by x, then by 0.80, and the result is 160 . 400×x×0.80=160
Multiply by 0.5 means reduce by 50%
If the diagonal of a square is 12 cm, then what is the area (in cm2 ) of the square?
Area of square =side2
ATQ, Diagonal =12cm Side ×√2=12
So, Side =12√2 Therefore, Area
A line passing through (3, 5) makes angle of 135∘ with x-axis. What will be its equation?
⇒ A (3,5)
(y-5)=-(x-3)
Equation of line
x+y-8=0
Three toys are in the shape of a cylinder, hemisphere, and cone. The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere, and cone, respectively?
= radius of each toy =2√2 slant height of cone
ratio = T.S.A of cylinder : T.S.A of hemisphere : T.S.A of cone =2πr(h+r):3πr2:πr(l+r)
=2(h+r):3r:(l+r)
=2(4√2):3×2√2:(4+2√2)
= 4 : 3 : √2 + 1
A sum of Rs 4000 becomes Rs 5800 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with the ame yearly interest rate (compounding of interest is done yearly), then what will be the amount (in Rs) after 2 years?
Average of the runs of 133 players of a team is 38. If the average of the runs of the male players is 43 and the average of the runs of the female players is 24, then what will be the ratio of the total runs of male players and the total runs of female players respectively?
M:F=14:10=14:5
No. of males
=(14/19)×133=98
Total runs of males
=98×43
No. of females
=133−98=35
Total runs of females
=35×24
Required ratio = (98 x 43)/(35 x 24) = 301/60
Argument and which is a 'weak' argument and choose the corresponding option as your answer.
Should religion be taught in schools in a secular state?
I. No, because in a secular state, indoctrination of children would be wrongful.
II. Yes, religion helps in inculcating moral values in a child.
Identify the diagram that best represents the relationship among the given classes.
Toys, plastic, wood
Three years ago, the average age of a family of 5 members was 17 years. The current average age of the family is equal to the average age of the family 3 years ago, due to the birth of a child. What is the present age of the child?
Total age of the family now = 17 x 6 = 102 years
Total age of the family excluding the child now = 85 + 15 = 100 years
Age of the child = 2 years
Seven people A, B, C, D, E, F, G were standing in a row according to their age in decreasing order such that the eldest person was standing in the front. Further it is known that G who was elder to F was standing adjacent to A. C was second youngest and was standing just behind E. F was not the youngest while D was standing at the front. A was not standing adjacent to D. How many people were standing between A and B?
D > ___ >___>___> E > C> ___
Now G was elder to F and adjacent to A. Also A was not seated adjacent to D.
D > G > A > ___>E > C >___
Since F was not the youngest. Hence
D > G > A > F > E > C > B.
So three people were seated between A and B.
If AMPHIBIOUS is written as MAHPBIOISU then how will ANTIBIOTIC be written as?
Which of the following will be the mirror image of the given question figure, if a mirror is placed along the line MN.
In each of the questions below, an assertion (a) is given, followed by a reason (R) which may or may not explain the assertion. From the given options, choose the right answer.
A: When we chew rice for a long time, it begins to taste sweet.
R: Ptyalin, an enzyme contained in saliva, breaks down starch into glucose.
A boy started walking straight for 5 kms. Then he took a right turn and walked for 2 kms. Then he again turned right and walked for 10 kms. Then he turned to his left and walked for 3 kms. It was the time for sunset and he observed that his shadow falls to his left. In which direction was he facing when he started walking from the starting point?
A two-digit number is 20% more than the number, which is the reverse of that number. What is the number?
The reverse number is 10b+a
10a+b= (10b+a) [1+(20/100)]
10a+b= (10b+a) [6/5]
50a+5b= 60b+6a
44a= 55b
4a= 5b
a/b = 5/4
Hence the number is 10a+b = 10x5+4 = 54
F is the brother of A. C is the daughter of A. K is the sister of F, G is the brother of C. who is the uncle of G ?
Mark the correct option based on which statement/statements are sufficient to answer the question.
How many sisters does Ramya have?
I. Antara is the sister of Ramya and is the youngest in the family
II. Ramya who is Sita's sister, has two siblings
From I
So statement I only is not sufficient to answer the question.
From II.
So statement II only is not sufficient to answer the question.
From 1 and 11
So we cannot answer how many sisters Ramya has because we do not know the gender of Sila.
Please note in reasoning questions one cannot assume the genders of a the the person even if they have names that are very commonly used for a male or female.
So, option d is the correct answer.
In each of the questions below, two statements are given, followed by two conclusions. You have to consider the given statements as true, even if they are at variance from commonly known facts. From the given options, choose the one that provides the correct combination of conclusions that follow/ can be derived from the given statements.
Statement A: Vineyards flourish, and wine is made in all parts of the kingdom.
Statement B: But that wine which is imported so largely into England, is made only from the grapes grown on the steep hillsides, as they are the finest of the lot.
Conclusions:
I: Only the wine made from the finest grapes is imported largely into England from the kingdom.
II: Wine is made only from grapes grown on steep hillsides.
73 + 31 = 104
54 + 31 = 85
63 + 21 = 84
In each of the following questions, select a figure from amongst the four alternatives, which when placed in the blank space of figure (X) would complete the pattern.
Identify the figure that completes the pattern.
In the following question, which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?
b _ d e _ b c _ e f _ c _ _ f b _ d _ f
A is the father of C and D is son of B. E is brother of A. If C is sister of D, how is B related to E?
Clearly B is the sister - in - law of E.
In the following question, four figures marked A, B, C and D, are given. Among these, three figures follow the same pattern and remaining one figure doesn't follow that pattern and hence, is odd. Mark the option which denotes the odd figure.
In each of the questions below are given some statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts.
Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements:
Some petals are corals.
No coral is a deal.
No petal is a steel.
Conclusions:
I. No deal is a coral.
II. Some deals are steels.
How many triangles are present in the given figure?
On one side of diagonal AP triangles are- ABE, ACF, ADJ, ADP, CDG, CDK, DGK, DJP, KOP = 9 triangles
So, on both sides = 2x9= 18 triangles.
But, apart from these 18, we have-
ABH, ACL, PNK, PMD = 4 triangles.
Thus, we have total triangles = 18+4= 22 triangles in the given figure.
Select the answer figure from the given alternatives, which can be formed by folding the given question figure?
6 lies opposite 3.
2lies opposite 4
1 lies opposite 5
1 and 5 cannot be on the adjacent faces.
6 and 3 cannot be on the adjacent faces.
A class consists of 180 students, 50 % passed in Maths, 10% students failed in Maths and English and 20% students passed in both Maths and English. Find the number of students passed only in English
Failed in both = 10% of 180
=> 18
=> Passed in both = 20% of 180
=> 36
=> Passed in maths = 50% 0f 180
=> 90
=> Passed only in math = 90-36
=> 54
=> Passed only in English = 180 - (54 + 36 + 18)
=> 72
A plece of paper is folded and cut as shown in the figure:
How will it appear when it is unfolded?
After 2nd unfolding
So, option 2 is the correct answer.
The series is given, with one term missing. Choose amongst the given responses and complete the series.
AZP, CWR, ETT, GQV, __.
2nd letter of each term is shown by a line from Z to N.
3rd letter of each term shown by the dotted line from P to X.
So INX is the correct answer.
If A is directly proportional to the square of B, B is inversely proportional to the square of C, and C is directly proportional to D, then what will be the change in the value of A if the value of D is increased by 200%?
C is directly proportional to D
D increases by 200% so it becomes 3 times
So, C becomes 3 times.
B is directly proportional (1/C2) = 1/9
B becomes (1/9) times
A is directly proportional B2 = (1/9)2 = (1/81) times
A becomes (1/81) times.
In each of the following questions, you are given a figure (X) followed by four alternative figures (a), (b), (c) and (d) such that figure (X) is embedded in one of them. Trace out the alternative figure which contains fig. (X) as its part.
When the East India Company was formed, the Mughal emperor in India was_____ .
Which one of the following countries shares the shortest boundary with India?
The maximum canal irrigated area is in the state of:
The first meeting of India and _______________ Joint Committee on Border Haats was held in Agartala recently.
By which name/names is our country mentioned in the Constitution?
Under the Ayushman Bharat Yojana, Prime Minister Narendra Modi has inaugurated the first Health and Wellness Centre in -
Which of the following is called ring disease in plants?
The density of the gas is maximum at which of the following factors?
Which of the following animals do belong to the mollusca phylum?
The following component of a fluorescent lamp contributes maximum in making them costly is______?
The particular element that is used in preparing windows for X-Ray Tubes is_________?
Which among the following is the first phase in the sexual reproduction of organisms?
The blood circulation inside the body takes approximately _________ seconds.
The plants that have respiratory roots are called_________
A sound wave travels from east to west, in which direction do the particles of air move?
An electric fuse wire melts if the amount of current flowing through it is-
Which among the following sources are considered to be naturally rich in Iodine-
1. Table Salt
2. Sea-food
3. Dairy Products
The circuit element is used to block DC in an electronic circuit?
An element which changes the rate of a chemical reaction but does not undergo any change in itself, is called-
An anti-knocking compound that has been phased out in many countries so far is__________?
Only two elements are in liquid state at room temperature. They are:
Which one the following statements is correct about Sound Waves?
The study of living organisms and their surrounding environment in the outer space is known as__________?
Consider the following, in the case that a tourist plans to visit a hill station located at very high altitude also wishes to take along his Television Set-
1. Plasma TV
2. Cathode Ray Tube TV
3. LCD TV
Which are expected to work properly at very high altitudes?
What is the name of reproductive part of the plant?
Bacteria was observed for the first time by____________?
AIDS causing HIV principally infects_____________?
Which of the following is also called the spirit of salt?
For the reversibility of a cycle, there should be