The correct answer is option (D):
Rs. 64
Let the original price of mangoes per mango be $P$ rupees.
Let the original number of mangoes the man could buy for Rs. 40 be $N$.
The total cost is the price per mango multiplied by the number of mangoes.
So, the original total cost is $N \times P = 40$.
The price of mangoes is reduced by 20%.
The new price per mango is $P - 0.20P = 0.80P$.
With the reduced price, the man can buy 25 mangoes more for Rs. 40.
The new number of mangoes he can buy is $N + 25$.
The total cost with the reduced price is $(N + 25) \times 0.80P = 40$.
We have two equations:
1) $NP = 40$
2) $(N + 25)(0.80P) = 40$
Let's expand the second equation:
$0.80NP + 25 \times 0.80P = 40$
$0.80NP + 20P = 40$
From the first equation, we know that $NP = 40$. Substitute this into the expanded second equation:
$0.80 \times 40 + 20P = 40$
$32 + 20P = 40$
Now, we can solve for $P$:
$20P = 40 - 32$
$20P = 8$
$P = 8 / 20$
$P = 0.4$ rupees per mango (this is the original price).
Now, let's find the reduced price per mango:
Reduced price $= 0.80P = 0.80 \times 0.4 = 0.32$ rupees per mango.
Alternatively, we can find the original number of mangoes the man could buy for Rs. 40.
Using $NP = 40$ and $P = 0.4$:
$N \times 0.4 = 40$
$N = 40 / 0.4$
$N = 100$ mangoes.
With the reduced price, he can buy $N + 25 = 100 + 25 = 125$ mangoes for Rs. 40.
Let's check this: $125 \times 0.32 = 40$. This is correct.
The question asks for the reduced price of a basket that contains 200 mangoes.
The reduced price per mango is Rs. 0.32.
The reduced price of 200 mangoes = 200 mangoes $\times$ Rs. 0.32/mango
Reduced price of 200 mangoes = $200 \times 0.32 = 64$ rupees.
Let's re-check the steps.
Original price per mango = P
Original number of mangoes for Rs 40 = N
NP = 40
Reduced price per mango = 0.8P
New number of mangoes for Rs 40 = N + 25
(N + 25) * 0.8P = 40
0.8NP + 20P = 40
Substitute NP = 40:
0.8(40) + 20P = 40
32 + 20P = 40
20P = 8
P = 0.4 Rs per mango (Original price)
Reduced price per mango = 0.8 * 0.4 = 0.32 Rs per mango
We need the reduced price of 200 mangoes.
Reduced price of 200 mangoes = 200 * 0.32 = 64 Rs.
The final answer is Rs. 64.
The final answer is $\boxed{Rs. 64}$.