Question

2530 soldiers were sent out on a mission. Each army truck could carry a maximum of 55 soldiers. How many army trucks were needed to carry all 2530 soldiers?
(a) 44
(b) 45
(c) 46
(d) 47

Answer 1

Hint: Assume that there are 55 seats in a single army truck, and each seat is occupied by one soldier. Now, find the total number of seats required to carry all 2530 soldiers. To find the total number of trucks required to carry all the soldiers divide the total number of seats required to carry all the soldiers by the number of seats available in one truck.

Complete step-by-step solution
Here, we have been provided with the information that an army truck can carry a maximum of 55 soldiers. We have to find the total number of army trucks required to carry 2530 soldiers.
Now, let us assume that there are 55 seats in one army truck and each seat is occupied by one soldier. Therefore, using the unitary method we can say that to carry all the 2530 soldiers we will need 2530 seats. So, we need to find the total number of trucks whose sum of seats when taken, equals 2530.
Now, one army truck contains 55 seats. So, we have,
\[\Rightarrow \] Number of trucks whose sum of seats equals 2530 = \[\dfrac{2530}{55}=46\]
Therefore, to carry all the 2530 soldiers, 46 numbers of army trucks will be needed.
Hence, the option (c) is the correct answer.

Note: One may note that we have applied the basic unitary method to solve the question. Actually, this question is from the topic ‘ratio and proportion’. There can be another method also to solve the question. What we can do is we will assume the total number of trucks required to carry all the soldiers as ‘n’. Now, we will write the given information in proportion form as: - 1 truck: 55 soldiers: : n truck: 2530 soldiers which is equal to the expression: - \[\dfrac{1}{55}=\dfrac{n}{2530}\]. Hence, by cross – multiplication we will simplify the expression and get the value of n.