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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:00
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A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

M46-11

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B
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:00
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Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only
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GMAT Club Official Explanation:



The average rate over the two days is 240/14 ≈ 17.1. An average must lie between the individual rates. If the rate on the second day was r and the rate on the first day was r + 8, then the average of 17.1 must satisfy r < 17.1 < r + 8.

Now let's check the options:

I. 9

If r = 9, then r + 8 = 17. Both rates (9 and 17) are below the average of 17.1, which is not possible.

II: 14

If r = 14, then r + 8 = 22. The average of 17.1 lies between 14 and 22, so this is possible.

III: 19

If r = 19, then r + 8 = 27. Both rates (19 and 27) are above the average of 17.1, which is not possible.

Answer: B.
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:09
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taking avg of speed done on both day
a be speeed on day 1, b be speed on day 2
240/14 = 17.14
now seeing if the two days speed can make above average work
case 1 b = 9 , a= 17
not possible as avg cant be more than the max numebr

case 2 b = 14, a= 22
can be possible as avg lie betwenn both number

case 3 b =19, b = 27
not possible as avg cant be less than lower number

hence ans is B
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:16
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Let the second day rate be r
Then the first day rate be r+8

Let the farmer work h hr on day 1 and 14-h hr on day 2.

Total work:
(r+8)h +r(14-h) = 240

h = (240-14r)/8

Check each options:

I. r=9
h = 14 + hr
Not possible

II. r =14
h = 5.5

III. h =19
h = -26/8
Negative not possible

Only II works.

Answer: B
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:29
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Let the farmer's rate of clearing a field, in square meters per hour, on the second day be x square meters per hour.
The farmer's rate of clearing the field on the first day = (x + 8) square meters per day

Let us assume that the farmer spent y hours on second day.
The farmer spent 14-y hours on the first day.

(x+8)(14-y) + xy = 240 square meters

I. x = 9; 17(14-y) + 9y = 240; 238 - 17y + 9y = 240; -8y = 2; y = -1/4; Not feasible
II. x = 14; 22(14-y) + 14y = 240; 308 - 22y + 14y = 240; 8y = 68; y = 8.5 hours; Feasible
III. x = 19; 27(19-y) + 19y = 240; 513 - 27y + 19y = 240; 8y = 273; y = 273/8 = 34...; 14-y>=0; y<= 14

IMO B
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:34
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Let, farmer second day rate = x squre meters per hour
First day rate = x+8
Let, the farmer works for day 1 = t hours
And for day 2 = 14-t
Total area cleared = 240
(x+8)t+x(14-t)=240
xt+8t+14x-xt=240
8t+14x=240
t=(240-14x)/8

1. x=9
t=(240-14*9)/8=14.25
Both day time combined is only14 hours but we get he worked for 14.25 hours on day 1, then on day 2 he worked (-0.25) hours which is not possible..........No

2. x=14
t=(240-14*14)/8=5.5
On day 1 he worked 5.5 hours and on day 2, (14-5.5=8.5) hours . ........Valid

3. x=19
t=(240-14*19)/8=-3.25
We get a negative value of time which is wrong.......No

2 only
B
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:36
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Let day 1 rate be x and time be y
then day 2 rate is x-8 and time is 14-y

total=work in day 1 +day 2
xy+(x-8)(14-y)=240
solving we get
7x+4y=126
looking at the answer choice and see what works
1)x=19-8=1
try x=1
119 is not multiple of 4 so no
2)x=6;14-8=6
84 we get a value for y and multiple of 4
3)
x=19 (19-8=11)
does not work
so final answer is B
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:40
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First day's rate = r+8 hours worked the first day = t
Second day's rate = r hours worked the second day = 14 - t
Total work = 240

Total work = hours worked the first day * first day's rate + hours worked the second day * second day's rate
240 = t(r+8) + (14-t)r
240 = 14(r+8) - 8t
t = ( 14(r+8) - 240 ) / 8

Plugging in the values of r, the only one that gives an acceptable value (where the hours worked in the first day are >0 and <14) is II
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:40
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let X be farmer rate on 1st day , X-8 becomes the rate on 2nd day
a be the no of hours 1st day and b be the no of hours 2nd day
X*a+(X-8)*b=240
a+b=14
Option I X-8=9 so X=17
17a+9b=240 & a+b=14 solving a=14.25 & b=-0.25
b can't be negative

Option II X-8=14, X=22
22a+14b=240 & a+b=14 solving a=5.5 & b=8.5 Option satisfies

Option III X-8=19, X=27
27a+19b=240 & a+b=14 solving a=-3.25 & b=17.25
a can't be negative

So answer is B, II only
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:41
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RateTimeWork
D1R+8TTR+8T
D2R14-T14R-RT
Total14240

TR + 8T + 14R - RT = 240
4T + 7R = 120
T = 30-7R/4

Checking options

I R=9
T = 30 - 7*9/4 = 120-63/4 = 57/4 = 14.25
But total T = 14
Invalid

II R=14
T = 30 - 7*14/4 = 120-98/4 = 22/4 = 11/2 = 5.5
Valid

III R = 19
T = 30 - 7*19/4 = 120 -133/4 = -ve
Invalid

Answer B

Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:44
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A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?
I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

total work is 240
let t1+t2=14
given answer options are of day 2 work
we know day 1 work is day2 +8
use options
#1
if day 2 work is 9 then that of day 1 is 17
17*t1 + 9*(14-t1)=240
solve for t1 we get t1 >14 which is not possible
#2
22*t1+14*(14-t1)= 240
t1 = 5.5 so t2 = 8.5
sufficient
#2
27*t1 +19(14-t1)=240
-ve number not possible

OPTION B ;14 is correct
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:45
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answer is b

(y+8).y + y.(14-x)=240

y= no of units in day 2 done in 1 hr
x is no of hours worked on day 1
substituting the value given in option for y
option 1 x becomes more than 14 hrs hence eliminated
option 2 x and y satisfies
option 3 x becomes negative
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:52
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Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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Let rate of Day 1 = r and Day 2 = r - 8
Total work = 240 sq m in 14hrs

we can use the formula:
(hours on day 1) x r + (hours on day 2) x (r-8) = 240

Test 1: Day 2 = 9, r =9+8 = 17
h1 + h2 = 14, substitute in equation below
17h1 + 9h2 = 240 => h1 = 14.25, h2 = -0.75 NOPE

Test 2: Day 2 = 14, r = 14+8=22
h1 + h2 = 14, substitute in equation below
22h1 + 14h2 = 240 => h1 + h2 = 14 => h1 = 5.5, h2 = 8.5 WORKS

Test 3: Day 2 = 19, r = 19+8=27
h1 + h2 = 14, substitute in equation below
27h1 + 19h2 = 240 => h1 is negative NOPE

Only 2 works
Answer is B
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:57
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Work = Rate x Time
Total work 240 sq. in 14 hours
Attachments

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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:01
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ASSUMING THAT FARMER WORKED 7 HRS ON BOTH THE DAYS

TRYING WITH THE FIRST VALUE

DAY1- 9+8= 17 * 7HRS=133
DAY2- 9*7= 63
I IS NOT THE ANSWER ELEMINATING OPTION A & D

II
DAY 1- 14+8=22*7= 154
DAY 2- 14*7= 94
154+94= 252
CLOSEST TILL NOW

III WILL BE BW TOO MUCH SO OPTION B IS THE ANSWER
Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:03
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Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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Let the first day rate be r; the second day rate be (r-8)
Let hours worked on the first day be hi; and the second day be h2

Total time=h1+h2=14
Total area cleared = rh1+(r-8)h2=840
h1=14-h2

r(14-h2)+(r-8)h2=240
14r-8h2=240
8h2=14r-240
h2=(14r-240)/8
For value to be possible, h2 must be positive and ≤14

1) r2=9; r=17
h2=(14(17)-240)/8=-(1/4) - not possible.

2) r2=14; r=22
h2=(14(22)-240)/8=8.5 - possible

3)r2=19;r=27
h2=(14(27)-240)/8=17.25 - not possible.


Hence, OPTION B (II ONLY)
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:32
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IMO B

we can do it using tables

RATETIMEWORK
DAY 1 x+8t1(x+8)t1
DAY 2xt2xt2
TOTAL14240

now we have two eqns

t1+t2= 14
(x+8)t1 +xt2= 240

substitute 1 in eqn 2, it will be
(x+8)t1+ x(14-t1)= 240

so t1= (240-14x)/8

Now we test all value given in eqn that is x= 9, 14 and 19.
From 9, we get t11= 14.25, can not be because t1+t2= 14, so t1 has to be less than <14.
from 14 we get t1= 8.5, so could be.
from 19 we get t1= -3.25 it cant be negative.

so Only II one suffices.
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:46
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Assuming y amount of work is done on day 1 and 240-y on day 2, we have

y/x + 240-y/(x-8) = 14

Rearranging the above equation, 352x = 14x^2+8y

We are given three options for x-8. Substituting the value of x accordingly in the above equation, we can see that y is positive for 9 and 14 but turns negative for 19.

Therefore, Option D
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 11:06
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assuming D1 -> r+8, h D2 -> r, 14-h
acc to question: h(r+8) + (14-h)r = 240 => h = 120-7r/4
substituting values:
I -> r = 9 -> h = 57/4 = 14.25 -> which is greater than 14 hence not possible.
II -> r = 14 -> h = 22/4 = 5.5 - ok
III -> r = 19 -> h = -13/4 -> -ve time hence not possible.

hence, II only.
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12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 11:10
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rate on day1 (work time t1) be r, so rate on day2 r-8 (time t2)
given:
t1+t2=14
rt1+(r-8)t2=240
solving, 8t2=14r-240
now, as per options, r=17,22,27
for r=17, t2=-ve
for r=27, t2>14
so only r=22 possible.
thus r-8 is 14

Ans B
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