Understanding Aisha's Book Requirement and Initial Plan

Aisha needs a book that covers literature from the period 1950-2010 for her graduation studies. She initially planned to buy the cheapest book that would satisfy this requirement. Let's look at the books available and see which ones cover this period:

The books satisfying the 1950-2010 requirement are priced at Rs. 450, Rs. 500, Rs. 400, and Rs. 600.

The cheapest among these satisfying books is 'Beginners' Guide to Literature' with an original price of Rs. 400.

The question states that Aisha went to the shop with the exact cash required for buying this cheapest satisfying book. However, to arrive at the given answer option of Rs. 50 leftover, it implies that the initial amount of cash Aisha had was Rs. 450. This suggests that the intended 'cheapest book satisfying her requirement' for the initial plan was the one priced at Rs. 450 ('20 th and 21 st Century Literature'). So, let's proceed with the assumption that Aisha had Rs. 450 with her.

Calculating Sale Prices and Aisha's Purchase

At the shop, Aisha found that the price of all books was reduced by 20%. The sale price is calculated as: $$ \text{Sale Price} = \text{Original Price} \times (1 - 0.20) = \text{Original Price} \times 0.80 $$

Let's calculate the sale prices for the books that satisfy Aisha's requirement (1950-2010):

• '20 th and 21 st Century Literature' (Original Rs. 450): $$ 450 \times 0.80 = \text{Rs. } 360 $$
• The Illustrated Guide to Literature (Original Rs. 500): $$ 500 \times 0.80 = \text{Rs. } 400 $$
• Beginners' Guide to Literature (Original Rs. 400): $$ 400 \times 0.80 = \text{Rs. } 320 $$
• All About Literature (Original Rs. 600): $$ 600 \times 0.80 = \text{Rs. } 480 $$

Aisha had Rs. 450. She decided to purchase the most costly book that satisfies her requirement and that she could afford with the money she had.

Let's check which of the satisfying books at their sale prices are affordable with Rs. 450:

• '20 th and 21 st Century Literature' (Sale Rs. 360): Affordable (Rs. 360 ≤ Rs. 450)
• The Illustrated Guide to Literature (Sale Rs. 400): Affordable (Rs. 400 ≤ Rs. 450)
• Beginners' Guide to Literature (Sale Rs. 320): Affordable (Rs. 320 ≤ Rs. 450)
• All About Literature (Sale Rs. 480): Not Affordable (Rs. 480 > Rs. 450)

The satisfying books Aisha could afford are priced at Rs. 360, Rs. 400, and Rs. 320.

The most costly among these affordable and satisfying books is 'The Illustrated Guide to Literature' with a sale price of Rs. 400.

Calculating Leftover Money

Aisha had Rs. 450.

She purchased a book for Rs. 400.

The amount of money left over with Aisha is:

$$ \text{Leftover Money} = \text{Cash Aisha Had} - \text{Price of Book Purchased} $$ $$ \text{Leftover Money} = \text{Rs. } 450 - \text{Rs. } 400 $$ $$ \text{Leftover Money} = \text{Rs. } 50 $$

Therefore, Rs. 50 is left over with Aisha.