To make a contractual obligation, a company must make 90 units of a pr

Question

To make a contractual obligation, a company must make 90 units of a product in 7 days. Each employee, working at a constant rate, makes 2 units per day. In the final 2 days, 60 units remain to be made, so the company immediately hires a additional people, each of whom works at the same constant rate of r units per day. With the additional workers, the company meets its goal.

If a < r, select the values of a and r that are jointly consistent with the given information. Make only two selections, one in each column.

If a < r, select the values of a and r that are jointly consistent with the given information. Make only two selections, one in each column.

poojaarora1818 · Answer

Solution:

As we know, a company must produce 90 units in 7 days. Each employee, working at a constant rate, produces 2 units per day, and 60 units remain within the final 2 days. Let's assume the total number of initial employees as x.

So, we set up an equation as 2x.

No. of units already produced = 90-60 = 30 units

30 units produced in 7- 2 = 5 days

To find the initial no. of employees we set up an equation as work = rate * time----> 30 = 2x * 5 = 3.

Now, to calculate the units made in 2 days we will set up the equation as

2 days (2*3 + ar) = 60 units, we will get a* r = 24. And as we know a < r and the only value that matches up for a = 4 and r = 6.

Karanjotsingh · Answer

Given Information: 
1. The company must produce  90 units in 7 days. 
2. Each employee produces  2 units per day. 
3. In the first 5 days, 30 units are completed. Therefore,  60 units remain for the last 2 days. 
4. During the last 2 days, additional workers are hired, each producing $r$ units per day.
5.  Condition : $a < r$.

Step 1: Employees Working for the First 5 Days 
Let’s assume the company starts with $a$ workers. In 5 days:

\text{Units produced} = 5 \cdot 2 \cdot a = 10a 
This means:
 10a = 30 \implies a = 3

So, initially, there are  3 workers.

Step 2: Units Remaining in the Last 2 Days 
The remaining units to be produced are:
90 - 30 = 60

Step 3: Total Work Done in the Last 2 Days 
For the last 2 days, the initial $a = 3$ workers continue to work, and additional workers are hired. Total work done in 2 days is:
 \text{Total work} = (3 + \text{additional workers}) \cdot r \cdot 2

If $b$ is the number of additional workers, then:
 2 \cdot (3r + br) = 60

Solving for values consistent with $a < r$, we find that:
 a = 4 \quad \text{and} \quad r = 6

HarshavardhanR · Answer

Say,

Initial number of workers = n

In the final 2 days, 60 units remain to be made

So, in the first 5 days, 90 - 60 = 30 units were made.

So,

(n)*(r)*(5) = 30
=>(1) ->  (n)*(r) = 6

"a" workers were added. The work was completed on time.

So,

(n+a) *(r)*(2) = 60

Using (1),

(a)*(r) = 24

Also, we are given that a<r.

From the choices, the only possible answer choices are  (a,r) = (4,6).

Harsha

Kunal.lost · Answer

How I approached the problem:

60 units are yet to be made in 2 days. So 30 units were made in 5 days.

30/5 = 6 units per day. Therefore 3 employees working at 2 units per day (given).

Problem statement: We need 60 units in 2 days. So 30 units per day.

We already have employees to make 6 units per day. So we're 24 units per day short.

The only combinations from the table that fit our description are (4,6) and (6,4)

But, as we know that a<r, we can eliminate (6,4).

So we're left with  (4,6) .

Bismuth83 · Answer

1. The question asks us to  find a working combination of a and r .

2. Let n be the number of original workers.

3. It is known that in the first 5 days n workers made 90 - 60 = 30 units, with each of them making 2 units per day. In other words,  30 = (2 * n) * 5 \rightarrow n = 3 .

4. The final 2 days had  n + a = a + 3  workers that made 60 units, with a of them making r units per day. So,  60 = (a * r + 3 * 2) * 2 \rightarrow ar = 24 .

5. Know we can look at the answer options with this knowledge and that a < r.  4 * 4 = 16 < 24  and 24 isn't divisible by 5, which means r = 6 and a = 4.

6. Our answer will be:   a = 4 and r = 6  .

pappal · Answer

as per given condition in first 5 days only 30 units are produced i.e. 6 units/day 
since rate of each worker=2 units/day. so, no. of workers initially=3
now a additional workers are added to work at the rate of r units/day for the next two days to meet the lapse of 60 units.
hence 2(3*2+a*r)=60 or 12+2a*r=60
2a*r=48 or a*r=24
since a<r so only values that satisfy are  a=4 & r=6

To make a contractual obligation, a company must make 90 units of a pr

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Two-part Analysis (TPA) Questions

To make a contractual obligation, a company must make 90 units of a pr

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards