CBSE Class 10-Mathematics: Chapter –3 Pair of Linear Equation in Two Variables Part 4

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Question 9:

In an election contested between A and B, A obtained votes equal to twice the no. of persons on the electoral roll who did not cast their votes & this later number was equal to twice his majority over B. If there were Persons on the electoral roll. How many voted for B.


Let be the no. of votes for A & B respectively.

The no. of persons who did not vote



On solving we get,

Vote for

Question 10:

When 6 boys were admitted & 6 girls left the percentage of boys increased from . Find the original no. of boys and girls in the class.


Let the no. of Boys be

Girls be



On solving we get

Question 11:

When the son will be as old as the father today their ages will add up to years. When the father was old as the son is today. Their ages add up to years. Find their present ages.


Let the son’s present age be

Father’s age be

Difference in age

Of this difference is added to the present age of son, then son will be as old as the father now and at that time, the father’s age will be


Solving we get the value of x and y

Question 12:

A cyclist, after riding a certain distance, stopped for half an hour to repair his bicycle, after which he completes the whole journey of at half speed in 5 hours. If the breakdown had occurred farther off, he would have done the whole journey in hours. Find where the breakdown occurred and his original speed.


Let be the place where breakdown occurred

be the original speed

On solving, we get,

On solving, we get,

Question 13:

The population of the village is . If in a year, the number of males were to increase by and that of a female by annually, the population would grow to at the end of the year. Find the number of males and females in the village. Let the number of males of males be and females be


On solving 1 & 2 we get

No. of males =2600

No. of females