Assume that a company faces two mutually exclusive project options to invest

Project-1

The initial investment during the initial time period or i is $17,000 and when i=1, 2, and 3 the cash flows or CFs are $7450, $4B, and $3B respectively. The IRR is 0.13 and the interest rate or r is 10% or 0.10. Therefore, based on the mathematical formula to calculate the IRR, IRR={CFs/(1+r)^i}-Initial investment

Therefore, based on the mathematical formula to calculate the IRR, it can be stated:-

IRR={CF1/(1+r)^1}+{CF2/(1+r)^2}+{CF3/(1+r)^3}-Initial investment

0.13={$7450/(1+0.10)^1}+{$4B/(1+0.10)^2}+{$3B/(1+0.10)^3}-$17,000

0.13=($7450/1.10)+($4B/1.21)+($3B/1.331)-$17,000

0.13=$6772.72+$4B/1.21+$3B/1.331-$17,000

0.13=$4B/1.21+$3B/1.331-$10,227.28

0.13=($5.324B+$3.63B-$16471.136)/1.61051

0.13=($8.95B-$16471.136)/1.61051

0.21=$8.95B-$16471.136

$16471.136+0.21=$8.95B

$16471.346=$8.95B

$16471.346/$8.95=B

$1840.374 approximately=B

Hence, the value of B, in tis case is approximately $1840.374 which is closes to $2000s given in one of the answer choices or options in the question.

Project-2

The initial investment in time period i=0 is $23,000 and the CFs in time period i=1,2, and 3 are respectively $9920, $5B, and A. The interest rate or r is 10% or 0.10 and the IRR is 0.17. Now, plugging the value of B obtained from the IRR calculation of project-1 into the CF of i=2, we get=$5*($1840.374)=$9201.87.

Therefore, again using the mathematical formula to calculate the IRR, we can get:-

IRR={CF1/(1+r)^1}+{CF2/(1+r)^2}+{CF3/(1+r)^3}-Initial investment

0.17={$9920/(1+0.10)^1}+{$9201.87/(1+0.10)^2}+{$A/(1+0.10)^3}-$23,000

0.17=($9920/1.10)+($9201.87/1.21)+($A/1.331)-$23,000

0.17=$9018.18+$7604.85+$A/1.331-$23,000

0.17=$A/1.331-$6376.97

$6376.97+0.17=$A/1.331

$6377.14=$A/1.331

$10,487.97 approximately =$A

Thus, the value of $A is approximately $10,487.97 which is closest to $11,600, in this case. Therefore, the answer here would be option c. given in the answer choices or options or A=11600, b=2000 approximately.