Page 173 - Maths Class 06

Application of Algebraic Equations
EX AM PLE 1. The num ber of boys in a school is 242 more than the num ber of girls. If the to tal num ber of
the stu dents in the school is 1200. Find the num ber of boys and girls in the school.

SOLUTION : Let the number of the girls in the school is x, then the number of the boys in the school is
x + 242.

\ x + 242 + x = 1200

Þ 2x + 242 = 1200
Þ 2x = 1200 242- [Transposing + 242 to RHS]

Þ 2x = 958
958
Þ x = [Dividing both side by 2]
2

Þ x = 479
\ Number of the girls in the school is 479 and number of the boys in the school is

(479 + 242 ) 721= .

EX AM PLE 2. A man is 4 times as old as his daughter. After 16 years he will be twice as old as his
daugh ter. Find their pres ent ages.

SOLUTION : Let daughter’s present age be x years

Then, her father’s present age = 4x years
)
Daughter’s age after 16 years =(x + 16 years
Father’s age after 16 years =(4x + 16 years
)
\ 4x + 16 = 2(x + 16)
Þ 4x + 16 = 2x + 32

Þ 4x - 2x = 32 16 [Transposing 2x to LHS and 16 to RHS]
-
Þ 2x = 16
16
Þ x = [Dividing both sides by 2]
2

Þ x = 8

\ Daughter’s present age = 8 years.
And her father’s present age =(4 ´ )8

= 32 years.

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