2 trucks and 4 vans can transfer the entire
goods in 4 days. 5 trucks and 6 vans can
transfer the same goods in 2 days. Then the
efficiency of 2 vans is equal to the efficiency
of how many trucks?
Answers
Given :- 2 trucks and 4 vans can transfer the entire goods in 4 days. 5 trucks and 6 vans can transfer the same goods in 2 days. Then the efficiency of 2 vans is equal to the efficiency of how many trucks ?
Solution :-
→ 2T + 4V can tranfer the goods in = 4 days .
and,
→ 5T + 6V can tranfer the same goods in = 2 days .
so,
→ 4(2T + 4V) = 2(5T + 6V)
→ 8T + 16V = 10T + 12V
→ 16V - 12V = 10T - 8T
→ 4V = 2T
→ V/T = 2/4
→ V/T = 1/2
→ V : T = 1 : 2 (Efficiency ratio)
then,
→ Efficiency of T = 2 unit / day
→ Efficiency of V = 1 unit / day
→ Efficiency of 2V = 2 * 1 = 2 unit / day
therefore,
→ Efficiency of 2V = 2 unit / day = Efficiency of T .
Hence, the efficiency of 2 vans is equal to the efficiency of 1 trucks .
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Given : 2 trucks and 4 vans can transfer the entire goods in 4 days.
5 trucks and 6 vans can transfer the same goods in 2 days.
To Find : the efficiency of 2 vans is equal to the efficiency of how many trucks
Solution:
Assume that efficiency of 2 vans is equal to the efficiency of x trucks
=> 2vans work = x truck work
=> 4 vans work = 2x truck work
=and 6 vans work = 3x truck work
2 trucks and 4 vans can transfer the entire goods in 4 days.
=> 2 trucks and 2x trucks can transfer the entire goods in 4 days.
=> 2(x + 1) trucks can transfer the entire goods in 4 days.
=> Total work done = 4 * 2(x + 1) = 8x + 8
5 trucks and 6 vans can transfer the entire goods in 2 days.
=> 5 trucks and 3x trucks can transfer the entire goods in 2 days.
=> 3x + 5 trucks can transfer the entire goods in 2 days.
=> Total work done =2 * (3x + 5) = 6x + 10
Equate total Work.
8x + 8 = 6x + 10
=> 2x = 2
=> x = 1
Hence efficiency of 2 vans is equal to the efficiency of 1 Truck
Verification :
2 trucks and 4 vans = 2 trucks and 2 trucks = 4 trucks in 4 Days
= 16 truck days
5 trucks and 6 vans = 5 trucks and 3 trucks = 8 trucks in 2 Days
= 16 truck days
Verified.
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