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Tarun had to prepare the document for his meeting urgently but he was hardly pressed for time.

Q29. The respective ratio between the ages of Samir, Joy and Pradeep is 16 : 14 : 13, The sum of their ages is 86. What will be the respective ratio between their ages 4 years hence?

The height of an equilateral triangle is $4\sqrt{3}$cm. The ratio of the area of its circumcircle to that of its incircle is -

The average incomes of the people in two villages are P and Q, respectively. Assume that $P\ne Q$. A person moves from the first village to the second village. The new average incomes are P' and Q', respectively. Which of the following is not possible?

Consider the marks obtained by 20 students out of 100 marks in a science quiz

30 40 50 35 55 60 40 30 60 75

75 60 30 40 60 55 35 50 40 30

What is the frequency of 60 marks out of 100?

Which of the following would be the step I?

Eight years ago, Raghav was four times as old as his brother Pankaj. Four years hence, Raghav's age will exceed his brother's age by $6$ years. The ratio of the present ages of Raghav and his brother is

5 men or 8 women can reap a field in 12 days. Find the number of days (approximately) taken by 3 men and 4 women to reap the same field.

The intensity of light produced by a light source varies inversely as the square of the distance from the source. If the intensity of light produced 3 feet from a light source is 750 foot-candles, find the intensity of light produced 5 feet from the same source. [4 MARKS]

A firm has tractors of four models A, B, C and D. Four tractors (two of model B and one each of models C and D) plough a field in 2 days. Two model A tractors and one model C tractor take 3 days to do this job. Three tractors one each of models A, B and C take 4 days to do the same task. How long will it take to do the job if a team is made up of four tractors of different models?

There are 4 routes between Delhi and Patna. In how many different ways can a man go from Delhi to Patna and return, if for returning

(i) any of the routes is taken;

(ii) the same route is taken ;

(iii) the same route is not taken ?

Solve the following.

The length of the shadow of an electric pole is 20m. At the same time, the length of the shadow of a tree of height 6m is 8m. Find the height of the electric pole.

If the ratio of marks obtained by Ankit in the internals of all three subjects (Economics, Finance and Accounts) in that order is 9:3: 4, then what was the ratio of marks scored by Sachin in the externals of those three subjects in the same order?

In a shooting competition, a marksman receives Rs.1 if he hits the mark and pays 30 paise if he misses it. He tried 50 shots and was paid Rs.11. How many times did he hit the mark?

At what time, between 3 o'clock and 4 o'clock, will both the needles coincide with each other?

The elevation of a tower at a station A due north of it is ${45}^{\circ }$ and at a station B due west of A is ${30}^{\circ }$. If AB = 40 m, find the height of the tower:

The total export of rice in 1994 was what percent of the total export in the year 1991 and 1993 ?

Find the next number in the sequence.

14, 28, 20, 40, 32, 64, __

A sphere of radius 13 cm is cut by a plane whose distance from the centre of the sphere is 5cm. What is the circumference of the section so obtained?

Let S be the set of all pairs (i,j) where 1$\le$ i < j $\le$ n and n$\ge$ 4. Any two distinct members of S are called friends, if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n=4, then S={(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}. Here (1,2), (1,3) are friends but (1,4), (2,3) are enemies.
For a general 'n', how many enemies will each member of S have?

Neha Gupta is a Science graduate passed in 2008 with 47% at the age of 24 years. She had scored 64% marks in HSC. She has also passed M.Sc. with 58% marks. She has done a certificate course in computers.