CHAIN RULE - SIMPLE PROBLEMS

SIMPLE PROBLEMS

1)If 15 toys cost Rs.234, what do 35 toys cost ?

Sol: Let the required cost be Rs. x then
more toys more cost(direct proportion)
15:35:: 234:x
(15*x)=(234*35)
x=(234*35) /(15)= 546 Rs

2)If 36 men can do a piece of work in 25hours, in how many hours will
15men do it?

Sol: Let the required number of hours be x.
less men more hours(Indirect proportion).
15:36::25:x
(15*x)=(36*25)
x=(36*25) /15
x=60
For 15 men it takes 60 hours.

3)If 9 engines consume 24metric tonnes of coal, when each is working
8 hours a day, how much coal will be required for 8 engines, each
running 13 hours a day, it being given that 3 engines of former type
consume as much as 4 engines of latter type?

Sol: Let 3 engines of former type consume 1 unit in 1 hour.
4 engines of latter type consume 1 unit in 1 hour.
1 engine of former type consumes 1/3 unit in 1 hour.
1 engine of latter type consumes ¼ unit in 1 hour.
Let required consumption of coal be x units.
Less engines, less coal consumed.(direct)
More working hours, more coal consumed(direct)
Less rate of consumption, less coal consumed (direct)

9:8
8:13 :: 24:x
1/3:1/4

(9*8*(1/3)*x)=(8*13*(1/4)*24)

24x=624

x=26 metric tonnes.