A person X was driving in a place where all roads ran either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other in a parallel. He started at the intersection of two roads, drove 3 km north, 3 km west and 4 km south. Which further route could bring him back to his starting point, if the same route is not repeated?

A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is

AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of $12$ meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of $5$ meters from A, then the original height of the trunk is

An agricultural field is in the form of a rectangle having length $X1$ meters and breadth $X2$ meters ($X1$ and $X2$ are variable). If $X1 + X2 = 40$ meters, then the area of the agricultural field will not exceed which one of the following values?

If R and S are different integers both divisible by 5, then which of the following is not necessarily true?

Anita’s mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is

A person walks 12 km due north, then 15 km due east, after that 19 km due west and then 15 km due south. How far is the from the starting point?

A person allows a 10% discount for cash payment from the marked price of a toy and still he makes a 10% gain. What is the cost price of the toy which is marked Rs. $770$?

A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.2 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability that the arrows fall in the red region of the archery target?

There are five hobby clubs in a college – photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within $180$ days?

A class starts at 11:00 am and lasts till 2:27 pm. Four periods of equal duration are held during this interval. After every period, a rest of 5 minutes is given to the students. The exact duration of each period is

30 g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar was mixed in 280 ml of water in vessel B and 20 g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is

A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the shuttle service?

In a class, there are 18 very tall boys. If these constitute threefourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

Four friends A, B, C, and D need to cross a bridge. A maximum of two persons can cross it at a time. It is night and they just have one lamp. Persons that cross the bridge must carry the lamp to find the way. A pair must walk together at the speed of the slower person. After crossing the bridge, the person having faster speed in the pair will return with the lamp each time to accompany another person in the group. Finally, the lamp has to be returned at the original place and the person who returns the lamp has to cross the bridge again without the lamp. To cross the bridge, the time taken by them is as follows : A: 1 minute, B: 2 minutes, C: 7 minutes and D : 10 minutes.

What is the total minimum time required by all the friends to cross the bridge?

A and B walk around a circular park. They start at 8 am from the same point in the opposite directions. A and B walk at a speed of $2$ rounds per hour and $3$ rounds per hour respectively. How many times shall they cross each other after 8:00 am and before 9:30 am?

In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of Rs. 2 by one student only, the total collection is Rs. 443. Then how many students are there in the class?

The monthly average salary paid to all the employees of a company was Rs. $5000$. The monthly average salary paid to male and female employees was Rs. $5200$ and Rs. $4200$ respectively. Then the percentage of males employed in the company is

Four-digit numbers are to be formed using the digits 1, 2, 3 and 4; and none of these four digits are repeated in any manner. Further,

1. 2 and 3 are not to immediately follow each other.
2. 1 is not to be immediately followed by 3.
3. 4 is not to appear at the last place.
4. 1 is not to appear at the first place.

How many different numbers can be formed?

Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long wouldRam take to complete the entire job alone?

A cylindrical overhead tank of radius 2 m and height 7 m is to be filled from an underground tank of size 5.5 m × 6 m. How much portion of the underground tank is still filled with water after filling the overhead tank completely?

A piece of tin is in the form of a rectangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is

The average monthly income of a person in a certain family of 5 is Rs. 10,000. What will be the average monthly income of a person in the same family if the income of one person increased by Rs. 1,20,000 per year?

W can do $25\%$ of a work in 30 days, X can do $\frac{1}{4}$ of the work in 10 days, Y can do $40\%$ of the work in 40 days and Z can do $\frac{1}{3}$ of the work in 13 days. Who will complete the work first?

There is an order of 19000 quantities of a particular product from a customer. The firm produces 1000 quantity of that product per day out of which 5% are unfit for sale. In how many days will the order be completed?

In a class of 60 students, where the number of girls is twice that of boys, Kamal, a boy, ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is

A person climbs a hill in a straight path from point ‘O’ on the ground in the direction of north-east and reaches a point ‘A’ after travelling a distance of $5$ km. Then, from the point ‘A’ he moves to point ‘B’ in the direction of north-west. Let the distance AB be $12$ km. Now, how far is the persons away from the starting point ‘O’?

The total emoluments of two persons are the same, but one gets allowances to the extent of $65\%$ of his basic pay and the other gets allowances to the extent of $80\%$ of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is

How many numbers are there between 100 and 300 which either begin with or end with 2?

Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the numbers X?