Exercise

Sushil runs four kilometres every day. On Saturday and Sunday he runs one kilometre extra (on each day). How many kilometres does he run in 2 weeks ?

Required distance that was covered

= 2 (5 x 4 + 2 x 5) km.

= 2 x 30 = 60 km.

The angles in a triangle are in a ratio of 1 9 : 1 0 : 7. What is the sum of twice the smallest angle and the largest angle ?

Sum of the angles of a traingle = 180^{o}

∴ 19x + 10x + 7x = 180^{o}

= 36x = 180^{o}

= x = 180^{o}/36 = 5^{o}

Required sum = 2 x 7x + 19x = 33x = 33 x 5 = 165^{o}

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

Let somu's age be x and the of his father be 3x.

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

If the numberator 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 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:

The following bar-graph show the production of foodgains in the three rice-producing states of India for the period 2004 to 2008.

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