​Rohan purchased an item for which there was a 13.5% discount offered on the part of the payment made in cash and a 6.25% surcharge on the part of the payment made through a credit card. If Rohan would have paid the entire amount in cash he would have paid Rs y for the item. But he actually had to pay Rs 40964 in all for the item, out of which Rs 29064 was paid in cash. What is the value of y?​

Correct option is D

Given:
Cash payment part = ₹29,064
Total amount paid = ₹40,964
Discount on cash payment = 13.5%
Surcharge on credit card payment = 6.25%

Solution:

Let the original price of cash payment 100%. 

After discount on cash payment 13.5%.

100% - 13.5% = 86.5%

86.5% = 29,064

% = $$\frac{29064}{86.5}$$

% = 336

100% = 33600

Amount paid in cash = 33600

Amount paid through credit card = 40964 − 29064 = ₹11900

Let the original price by credit card = 100%

After surcharge on credit card payment 6.25% = 100% + 6.25% = 106.25%

106.25% = 11900

% = $$\frac{11900}{106.25} = 112$$

100% = 11200

Amount paid in credit card = 11200

Sum of the original prices = Paid in cash + Paid by credit card

Sum of the original prices = 33600 + 11200 = 44800

Entire amount in cash (y) = $$\frac{100-13.5}{100}\times 44800 = \frac{86.5}{100}\times 44800$$

Entire amount in cash (y) = 38752​​

So, the value of y is ₹38752.

Thus, the correct asnwer is (d).