ABC is a triangle and AD is perpendicular to BC. It is given that the lengths AB, EC, CA are all rational numbers. Which one of the following is correct?
Consider those numbers between 300 and 400 such that when each number is divided by 6, 9 and 12 it leaves 4 as remainder in each case. What is the sum of the numbers?
What is the value of \[\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{4}}\]is
Two trains 130 m and 110 m in length are running towards each other on parallel tracks, one at the rate of 32 km/h and another at 40 km/h respectively in what time will they be clear each other from the moment they meet?
A fort has provision for 220 soldiers for 16 weeks at the rate of 45 g per day. How many soldiers should go out so that the provision may last for 24 weeks at the rate of 33 g per day?
In an examination 42% candidates failed in Hindi and 52% failed in English. 17% failed in both the subjects. If 69 candidates passed in both the subjects. What is the total number of candidates appeared?
A man gives 20% of his money to his eldest son. 36% of the remaining he gives to b his younger son. 10% of the remaining he gives in a school for poor boys. Still he has Rs. 100.80. Find his total sum
A can complete a work in 30 days while B can complete the same work in 40 days. If the work together, men in now many days will they complete the work?
Vinod was engaged on the condition that he will get Rs. 50 per day when he works. But he will be find Rs. 5 per day when he is absent. If after 30 days he gets 950 in all for how many days did he remain absent?
Two pipes can fill a cistern in 12 min and 15 min respectively. A third pipe can empty the cistern in 20 min. How long will it take to fill the cistern if all the three pipes are opened at the same time?
Two tap A and B can fill a cistern in 16 min and 24 min respectively. How much after opening the both taps the tap B should be turned off so that the cistern may take 12 min to fill?
A train 100 m long is running at the speed of 21 km/h and another train 150m long is running at the speed of 36 km/h in the same direction. How long will the faster train take to pass the first train?
Ram covers a certain distance by train at 25 km/h and the same distance on foot at 4 km/h. If the time taken by him for the whole journey be 5 h and 48 min, how much total distance did he cover?
Two equal glasses are \[\frac{1}{3}\]and \[\frac{1}{4}\]full of milk respectively. They are completely filled up with water. The contents are then mixed up in another vessel. What will be the ratio of milk and water in the vessel?
A and B enter into a partnership with capital in the ratio of 5 : 6. After 8 months, A withdraws his capital. If their shares in profit are in the ratio of 5 : 9, then for how much time the capital of B remained in the business?
Ramu started a business with Rs. 75000: After 4 months Monu also joined him with Rs.112500. If at the end of the year the total profit is Rs. 22500, Mom share will be
Pressure varies inversely as volume varies and temperature varies directly as volume varies. At a time volume \[=50\,\,{{m}^{3}},\]temperature =25 K and pressure = 1 atm. If volume is increased to \[200\,\,{{m}^{3}},\]then the temperature will be
The length and breadth of a square are increased by 40 % and 20%, respectively. Find the difference of area the rectangle so formed to the original square
A student moves \[\sqrt{2}\,\,x\,\,km\] East from his residence and then moves \[x\,\,km\]North. He then goes x km North-East and finally he takes a turn of \[90{}^\circ \] towards right and moves a distance \[x\,\,km\] and reaches his school. What is the shortest distance of the school from his residence?
A person invested some amount at the rate of 12% simple interest and the remaining at 10%. He received yearly an interest of Rs. 130. Had he interchanged the amounts invested, he would have received an interest of Rs. 134. How much money did he invest at different rates?
A)
Rs. 500 at the rate of 10%, Rs. 800 at the rate of 12%
doneclear
B)
Rs. 700 at the rate of 10%, Rs.600 at the rate of 12%
doneclear
C)
Rs.800 at the rate of 10%, Rs. 400 at the rate of 12%
doneclear
D)
Rs. 700 at the rate of 10%, Rs. 500 at the rate of 12%
Three glasses of capacity 2 L, 5 L and 9 L contain mixture of milk and water with milk concentrations 90%, 80% and 70% respectively. The contents of three glasses are emptied into a large vessel. Find the milk concentration and ratio of milk to water in the resultant mixture
The diameter and slant height of a conical tomb are 28 m and 50 m respectively. The cost of white washing its curved surface at the rate of 80 paise per square metre is
The monthly incomes of two persons are in the ratio of 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves Rs. 500 a month, what are their monthly incomes?
If 7% of the sale price of an article is equivalent to 8% of its cost price and 9% of its sale price exceeds 10% of the cost price by Rs. 1, then what is the cost price of the article?
A daily wage worker was paid Rs. 1700 during a period of 30 days. During this period he was absent for 4 days and was fixed Rs. 15 per day for absence. He was paid the full salary only for 18 days as he came late on the other days. Those who came late were given only half the salary for that day. What was the total salary paid per month to a worker who came on time every day and was never absent?
The captain of a famous club cricket team of eleven members is 26 yr old and the wicket keeper is 3 yr older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
A leak was found in a ship when it was 77 km from the shore. It was found that the leak admits 2.25 tones of water in 5.5 min. 92 tones will suffice to sink the ship. But the pumps can throw out 12 tones an hour. Find the average rate of sailing at which the ship may reach the shore as she begins to sink
Rajdhani Express has a capacity of 500 seats of which 10% is in the Executive class, rest being chaircar. During one journey the train was booked to 85% of its capacity. If Executive class was booked to 96% of its capacity, how many chaircar seats were empty during that journey?
Two trains of length 100 m and 80 m respectively run on parallel lines of rails. When running in the same direction the faster train passes the slower one in 18 s, but when they are running in opposite directions with the same speeds as earlier, they pass each other in 9 s. Find the speed of faster train
A car driver travels from plain to hill station which are 200 km apart at an average speed of 40 km/h. In the return trip he covers the same distance at an average speed of 20 km/h. The average speed of the car over the entire distance of 400 km is
Anshul's age is\[\frac{1}{6}\] th of Brinda's age. Brinda's age will be twice of Celina's age after 10 yr. If Celina's 8th birthday was celebrated two years ago, the present age of Anshul is
Divide Rs. 900 among X, Y and Z so that Rs. 40 more than \[\frac{2}{5}\] th of X's share, Rs. 20 more than \[\frac{2}{7}\] th of Y's share and Rs. 10 more than\[\frac{9}{17}\]th of Y's share may all be equal. What ts X's share?
A shopkeeper bought a chair and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs. 55 more, he would have had a profit of 40%. What is the cost price of chair?
Sunita can do a piece of work in 6 h and Kavita alone can do it in 8 h. Sunita and Kavita under took to do it for Rs. 320. With the help of Geetanjali, they finished it in 3 h. How much is paid to Geetanjali?
Of the three numbers the sum of first two is 45, the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. Find out the third number
A person borrows Rs. 4000 from a co-operative ban at \[7\frac{1}{2}%\]compound interest. At the end of every year he pays Rs. 1500 as part repayment of loan interest. How much does he still owe to the co-operative bank after three such installments?
Two pipes X and Y can fill a tank in 36 min 45 min, respectively. A waste pipe Z can empty tank in 30 min. First X and Y are opened. After 7 min, Z is also opened. In how much time, the tank is full?
P, Q and R enter into partnership by making investments in the ratio 3 : 5 : 7. After a year R invests another Rs. 337600 while P withdrew Rs. 45600 ratio of investments, then changes to 24 : 59 : 167. How much did P invest initially?
The children in three societies are in the ratio 2 : 3: 5. If 10 children are increased in each society, the changes to 4 : 5 : 7. The total number of children before the increase were
Two factory workers Prakash and Saurabh are a total of Rs. 1650 per week by their employer. If Prakash is paid 120% of sum paid to Saurabh, how much is Saurabh paid per week?
The rate of interest on a sum of money is 4% per annum for the first 2 yr, 6% per annum for the next 4 yr and 8% per annum for the period beyond 6 yr. If the simple interest accrued by the sum for a total period of 9 yr is Rs. 2240, what is the sum?
A property dealer leaves 12900 sq yards area to be divided among his 5 brothers, 4 daughters and 2 sisters. If each daughter receives 4 times as much as each sister and each brother gets 5 times as much as each sister, then how much did each laughter get?
A rectangular courtyard of a temple 3.78 m long and 5.25 m wide is to be paved exactly with square marble stones, all of the same size. What is the largest size of the marble stone which could be used for the purpose?
In a mixture of 90 L, the ratio of milk and water is 2 : 1. If the ratio of the milk and water is to be 1 : 2, then the amount of water to be further added is
The sum of the ages of a mother and son is 45 yr. Five years ago the product of their ages was 4 times the mother's age at that time. The present age of the mother and son, respectively are
The ratio of males and females in a town is 7 : 8 Respectively and the percentage of children among males and females is 25% and 20%, respectively. If the number of adult females in the town is 235200. What is the total population of town?
Two super-fast trains P and Q start from stations A and B towards B and A respectively. After passing each other, they take 4 h 48 min and 3 h 20 min to reach B and A respectively. If the train P is moving at 45 km/h, then find the speed of train Q
Manishanker and Hariharan started a business investing amounts in the ratio of 2 : 3 respectively. If Manishanker had invested an additional amount of Rs. 10000 the ratio of Manishanker's investment to Hariharan?s investment would have been 3 : 2. What was amount invested by Manishanker?
Aniroodh deposited two parts of a sum of Rs. 25 000 in different co-operative banks at the rates of 15% per annum and 18% per annum respectively. In one year he got Rs. 4050 as the total interest. What was the amount deposited at the rate of 18% per annum?
The work done by a woman worker in 8 h is equal to the work done by a man worker in 6 h and by a boy worker in 12 h. If working 6 h/day 9 men worker, 12 women worker and 12 boys worker together finish the same work working 8 h/day?
Geetanjali bought two wrist watches for Rs. 720. She sold one at loss of 15% and the other at a gain of 19% and then her friend found that each wrist watch was sold at the same price. Find the cost of the wrist watch sold at a loss
A person covers a certain distance between his house and office on motorcycle. Having an average speed of 30 km/h, he is late by 10 min. However with a speed of 40 km/h, he reaches his office 5 min earlier. Find the distance between his house and office
X and Y entered into a partnership investing Rs. 16000 and Rs. 12000, respectively. After 3 months, X withdrew Rs. 5000 while Y invested Rs. 5000 more. After 3 more months Z joins the business with a capital of Rs. 21000. The share of Y exceeds that of Z, out of a total profit of Rs. 26400 after one year, by
In an exam, the average was found to be 50 marks. After deducting computational errors the marks of the 100 candidates had to be changed from 90 to 60 each and the average came down to 45 marks. The total number of candidates who took the exam were
The strength of a Day Boarding School increases and decreases every alternate year. It starts with increase by 10% and thereafter the percentage of increase/decrease is the same. Which of the following is definitely true about the strength of the Day Boarding School in year 2001 as compared to that in year1997?
A builder decided to build a farm house in 40 days. He employed 100 workers in the beginning and 100 more after 35 days and completed the construction in stipulated time. If he had not employed the additional workers, how many days behind schedule would it have been finished?
Two pipes P and Q can fill a tank in 15 h and 20 h respectively, while a third pipe R can empty the full tank in 25 h. All the three pipes are opened in the beginning. After 10 h, R is closed. The time taken to fill the tank is
Income of two business bourse P and Q are in the ratio of 5 : 8. Had the income of business house P been more by Rs. 50 lakh, the ratio of their incomes would have been 5 : 4 respectively. What is the income of business house Q?
Kimtilal gave Rs. 25000 to his 'eldest son' Ramlal, \[\frac{5}{12}\]of the whole property to the 'second son' Shyamlal and to the 'youngest son' Premlal as much as two the 'eldest son' Ramlal and the 'second son' Shyamlal together. How much did the 'youngest son' Premlal get?
A person starts going for evening walk everyday. The distance walked by him on the first day was 4 km. Everyday he walks half of the distance walked on the previous day. What can be the maximum total distance walked by him in his life time?
A wall clock which gains uniformly is 2 min slow at noon on Sunday and is 4 min 48 s fast at 2 pm on the following Sunday. When did it show the correct time?
Two men are on opposite sides of a tower. The measure the angles of elevation of the top of di tower as \[30{}^\circ \]and \[45{}^\circ ,\]respectively. If the height of a tower is 50 m, find the distance between the two men. (Take\[\sqrt{3}=1.73\])
A and B solved a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as 6 and 2, while B made a mistake in the coefficient of x only and obtained the roots\[-7\]and\[-1.\]Find the correct roots of the equation