(a) Moiz and Mair share a lottery win of Rs. 2000 in the ratio of 1:4. Moiz then shares this part between himself, his wife and his son in the ratio of 4:5:1. How much more does his wife get over his son? (b) A farmer keeps hens and rabbits on his farm. One day he counted a total of 70 heads and 196 legs. How many more hens than rabbits does he have? (c) What is polygon? Describe different types of regular polygon. (d) In a certain code computer is written as FRUVQNPC. How will MEDICINE be written in code language?

(a) Sharing the lottery win

Moiz's share = (1 ÷ 5) × 2000 = Rs. 400.

The ratio 4 : 5 : 1 has 10 parts, so one part = 400 ÷ 10 = Rs. 40.

Moiz keeps 4 × 40 = Rs. 160, his wife gets 5 × 40 = Rs. 200, and his son gets 1 × 40 = Rs. 40.

The wife gets 200 − 40 = Rs. 160 more than the son.

(b) Hens and rabbits

Let h be the number of hens and r the number of rabbits. Each animal has one head, a hen has 2 legs and a rabbit has 4.

h + r = 70 ... (1) 2h + 4r = 196 ... (2)

Doubling (1) gives 2h + 2r = 140. Subtracting this from (2) gives 2r = 56, so r = 28, and then h = 42.

Check: the legs come to 42 × 2 + 28 × 4 = 84 + 112 = 196.

He has 42 − 28 = 14 more hens than rabbits.

(c) Polygons

A polygon is a closed plane figure made up of three or more straight sides. A regular polygon has all sides equal and all interior angles equal.

Each interior angle of a regular polygon with n sides = (n − 2) × 180° ÷ n.

Common regular polygons

Equilateral triangle: it has 3 sides, each angle 60°. Square: 4 sides, each angle 90°. Regular pentagon: 5 sides, each angle 108°. Regular hexagon: 6 sides, each angle 120°, as in honeycomb cells. Regular heptagon: 7 sides, each angle about 128.6°. Regular octagon: 8 sides, each angle 135°, as in many stop signs. Regular nonagon: 9 sides, each angle 140°. Regular decagon: 10 sides, each angle 144°.

As the number of sides grows, a regular polygon comes increasingly to resemble a circle.

(d) Coding

Note on the printed code: the first two letters appear to have been swapped in this paper. A question with the same words in the 2017 paper gives COMPUTER as RFUVQNPC, which follows a clear rule, and FRUVQNPC does not follow any consistent one.

Rule from RFUVQNPC: reverse the word (RETUPMOC), keep its first and last letters, and move each letter in between one step forward in the alphabet.

MEDICINE reversed is E N I C I D E M. Keep E and M, and shift the middle letters: N→O, I→J, C→D, I→J, D→E, E→F.

MEDICINE is written as EOJDJEFM.