# 9. (A) Divide Rs.500 between Arham, Mariam and Sarim so that Arham gets 2/3 of what Mariam gets and Mariam gets ¼ of what Sarim gets. Find the share of each. (B) A school has enough provision of food for 52 days. After 20 days a group of 400 students arrives and the food would have last for 24 days only. How many students are there in the school actually?

## (C) A man walks 2km towards North. Then he turns to East and walks 10km. After this he turns to North and walks 3km. Again he turns towards East and walks 2km. How far is he from the starting point? (D) In a certain code language COMPUTER is written as RFUVQNPC. How will MEDICINE be written in that code language?

**A) Let’s assume the share of Mariam is x. Then, according to the given conditions**:

Arham’s share = 2/3 x Sarim’s share = 4x

Total share = Arham’s share + Mariam’s share + Sarim’s share = 500

**Substituting the values, we get:**

2/3 x + x + 4x = 500 7x = 500 x = 71.43 (approx)

Arham’s share = 2/3 x = 47.62 (approx) Mariam’s share = x = 71.43 Sarim’s share = 4x = 285.72 (approx)

Therefore, Arham’s share is Rs. 47.62, Mariam’s share is Rs. 71.43, and Sarim’s share is Rs. 285.72.

**B) Let’s assume there are x students in the school. Then, according to the given conditions**:

Food provision for x students = 52 days Food provision for 400 students = 24 days

**Using the formula “work = rate x time”, we can set up the following equation**:

x(52) = (x + 400)(24)

**Solving for x, we get:**

x = 2400

Therefore, there are 2400 students in the school.

**C) The man walks 2km towards North**, then 10km towards East, then 3km towards North, and then 2km towards East.

This forms a right-angled triangle, where the two legs are 2km + 3km = 5km and 10km + 2km = 12km.

Using the Pythagorean theorem, we can find the hypotenuse, which is the distance from the starting point:

Hypotenuse = sqrt(5^2 + 12^2) = sqrt(169) = 13km

Therefore, the man is 13km away from the starting point.

**D) Each letter of the word COMPUTER is shifted 2 positions to the right to get the corresponding letter in the code language. Using the same rule, we can write MEDICINE as:**

M + 2 = O E + 2 = G D + 2 = F I + 2 = K C + 2 = E I + 2 = K N + 2 = P E + 2 = G

Therefore, MEDICINE is written as OGFKEKP.