Page 153 - Maths Skills - 8

Direct and Inverse Proportions 151

MIND MAP

Direct and Inverse Proportions

Proportion

“Two quantities are in proportion if any increment or decrement in
one quantity results accordingly changes in the other”.

Indirect Proportion
Direct Proportion 1

x a y x a y
or x = ky (here, k contt.) k
y
x or x = (here, k contt.)
or y = k or xy = k

Time and Work

Time and Distance � If a person ‘A’ finish a work in m days, then the work done
1
Distance by A in 1 day is m .
1
� Speed = If a person A’s 1 day's work is , then person A can complete
Time � m
� 1 km = 1000 metre the work in m days.
� 1 hour = 3600 second � If A can complete the work in m days and B can do it in n
1
1
Problems Based Upon Trains days then A's 1 day work is m and B's 1 day work is n . Now
l m 1 day work of both of them is ( 1 + 1 )
1
l m m n
2
a m/s
b m/s ( l + l ) m
Time taken by the trains to cross each other = Total Distance = 1 2
a m/s, l m Total Time (a + b) m/s
1
b m/s, l m
2
Faster Train
Slower Train
Total Distance
Total Distance ( l + l ) m
1
2
Time taken to cross each other = =
Total Time (a – b) m/s