(A) The sum of two numbers is 48. If the smaller number is one-fifth of the larger number, find the two numbers. (B) Find out the correct word from the jumbled spellings given: IUPNRT, AERPSTEL, LLARIVTTOUE, DCAAOOV, ANAISSSOITANS. (C) A sphere of diameter 26 cm is half filled with honey. The honey is poured into a cylindrical beaker of diameter 16 cm. Find the depth of honey in the beaker. (D) The breadth, length, and height of a room is 14 feet, 20 feet and 10 feet respectively. There is also a door of room having height 8 feet and width 5 feet. Two windows of 4 feet by 5 feet are also there. The cost of paint and labour inside room is Rs. 100 per square foot. How much will it cost to paint the inner walls and roof of the room?

(A) The two numbers

Let the larger number be x, so the smaller is x/5.

x + x/5 = 48, so 6x/5 = 48, and x = 40.

The numbers are 40 and 8.

(B) Jumbled words

IUPNRT = TURNIP AERPSTEL = PRELATES (senior members of the clergy; the same letters also make PLEATERS) LLARIVTTOUE = ULTRAVIOLET DCAAOOV = AVOCADO ANAISSSOITANS = ASSASSINATION

(C) Depth of honey

The sphere's radius is 13 cm, and the beaker's radius is 8 cm. Half filled here means half of the sphere's volume.

Volume of honey = ½ × (4/3)πr³ = (2/3)π × 13³ = (2/3)π × 2,197.

Volume in the beaker = πR²h = π × 8² × h = 64πh.

Setting these equal, π cancels: h = (2/3 × 2,197) ÷ 64 = 1,464.67 ÷ 64 ≈ 22.9 cm.

(D) Cost of painting

Area of the four walls = 2 × (14 + 20) × 10 = 680 sq ft. Area of the roof = 14 × 20 = 280 sq ft.

Door = 8 × 5 = 40 sq ft. Two windows = 2 × (4 × 5) = 40 sq ft.

Area to paint = 680 + 280 − 40 − 40 = 880 sq ft.

Cost = 880 × 100 = Rs. 88,000.

The door's second measurement appears garbled in the copy of the paper available, and it is read here as a width of 5 feet.