Hey!
The quantity of woods carried by a buffalo cart in a certain time is 1/10 of that carried by a truck at the same time. If 3 trucks and 5 buffalo carts,working 8 hours a day, can carry 490 tons of wood, then how many trucks should be engaged with 12 buffalo carts to carry 3136 tons of woods in 7 days?
<> Expecting accurate answers!
Share
Verified answer
The quantity of woods carried by a truck = 10 × quantity of woods carried by buffalo .it means power for doing work of one truck = 10 × power for doing work of one buffalo .
we can say that ,
power of 10 buffalo = power of one truck .
or ,
we can say that
one truck = 10 buffalo .
now,
(3 truck + 5 buffalo ) can carry 490 tons of woods after working 8 hour in 1 day.
we know,
number of persons × number of days = number of work
so,
(3 truck + 5buffalo ) × 1 = 490
(3 truck + 5 buffalo ) = 490/1 [ Let all days they work 8 hours , so time is constant ] ---(1)
Let x truck require for doing work .
then,
(x truck + 12 buffalo ) can carry 3136 tons of woods after working 8 hours in 7 days
e.g.,
(x truck + 12 buffalo ) × 7 = 3136
(x truck + 12 buffalo ) = 3136/7 = 448 ----(2)
from equation (1) ÷ (2)
(3 truck + 5 buffalo )/(x truck + 12 buffalo ) = 490/448 = 70/64
64( 3 truck + 5 buffalo ) = 70(x truck + 12 buffalo )
192 truck + 320 buffalo = 70x truck + 840 buffalo
now, put 1 buffalo = 1/10 truck
192 truck + 32 truck = 70x truck + 84 truck
224 - 84 = 70x
140 = 70x
x = 2
hence, 2 truck require