Exercise

A basket contains 5 blue, 4 green and 3 red ball. If three balls are picked at random, what is the probability that at least one is red ?

Probability of having no red ball is

^{9}C_{3} / ^{12}C_{3} = 21/55

Probability of having at least one red ball is 1 - 21/55 = 34/55

The average of five consecutive odd numbers A, B, C, D and E is 25. What percent of E is C ?

In such a case the middle number (C) is the average

∴ C = 25 and F = 29

Required percentage = 25/29 x 100 = 86.2

The age of Somu is one-third his father's. 6 years back he was one-fifth of his father's age. What is his persent age ?

Let Somu's age be x and that of his father be 3x.

So, x - 6 = 3x - 6/5 = x = 12

If the numerator of a fraction is increased by 50% and denominator by 20%, the fraction become 9/15. What was the original fraction ?

Let the fraction be x/y

We have 150x/120y = 9/15

= x/y = 12/25

If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 18. If the sum of the two digits of the number is 14. What is the original number ?

Let the no. be 10x + y.

No. formed by the interchange of digits = 10y + x

We have y - x = 2 .....(i)

y + x = 14 .....(ii)

Solving (i) and (ii), we get x = 6, and y = 8

∴ the no. is 68.

Direction (Q. 6-10) : Study the following graph carefully and answer the questions that fallow:

What is the average production per year of rice in the three states during the given period ?

Reqd average = 63980/5 = 12796

What is the ratio of the total production of rice in Benga1 to that of rice in UP ?

Reqd ratio = 20900/23780 = 1045/1189

What is the percentage contribution of Bihar in the total production in 2008 ?

Reqd Percentage = 4300/14580 x 100 = 29.49

Production of rice in 2004 in what per cent of the production of rice in 2008 in all the three states ?

Reqd percentage = 10650/14580 x 100 = 73

What per cent of production in 2005 should be added to it to make it equal to the production in 2006 ?

Reqd percentage = 1550/12500 x 100 = 12.4