Chapter 1 · Practice set 1Textbook pages 10–11

Practice Set 1 – Animated Solutions ചിന്തിക്കാം

The textbook asks you to solve these eight puzzles mentally, with one letter, or with two equations – whichever you like. For each one, read the question, try it in your notebook (use the hint if you are stuck), then press Next ▶ and watch the solution grow.

📖 Tools you will use (pages 1–5 of this guide)

Question 1 · Bag and umbrella

Q1Priya bought a bag and an umbrella, paying ₹1100. The bag cost ₹300 more than the umbrella. What did each cost?

(പ്രിയ 1100 രൂപ കൊടുത്ത് ബാഗും കുടയും വാങ്ങി. ബാഗിന് കുടയെക്കാൾ 300 രൂപ കൂടുതലാണ്. ഓരോന്നിന്റെയും വില എത്ര?)

Put the extra ₹300 of the bag aside. What is left is shared equally.

🎬 Solution animation

🧠 In your head

1100 − 300 = 800, half is 400. Umbrella ₹400; bag 400 + 300 = ₹700.

✏️ One letter

umbrella x, bag x + 300 x + (x + 300) = 1100 2x = 800, x = 400

✏️✏️ Two letters

bag x, umbrella y x + y = 1100 x − y = 300 add: 2x = 1400, x = 700
Answer: umbrella ₹400, bag ₹700 (check: 400 + 700 = 1100, 700 − 400 = 300).

Question 2 · Sum 26, difference 4

Q2The sum of two numbers is 26 and their difference is 4. Find the numbers.

The larger is the smaller plus 4. Take the 4 away from 26 and halve.

🎬 Solution animation
Answer: 15 and 11. With two letters: x + y = 26, x − y = 4; adding gives 2x = 30.
🌍 Why this matters

"Sum and difference" puzzles hide everywhere – two brothers' ages, two sides of a field, two teams' scores. Section 3 (page 9 of this guide) turns this into a one-line rule.

Question 3 · A rectangle's sides

Q3The perimeter of a rectangle is 40 centimetres. One side is 8 centimetres longer than the other. Find the lengths of the sides.

Half the perimeter is one length plus one breadth.

🎬 Solution animation
Answer: the sides are 6 cm and 14 cm (check: 2 × (6 + 14) = 40).

Question 4 · One wire, a square and a triangle

Q4A wire 3½ metres long is cut into two pieces. One piece is bent into a square and the other into an equilateral triangle, and all the sides of both are equal. How should the wire be cut?

The square has 4 sides, the triangle 3 – seven equal sides in all.

🎬 Solution animation
Answer: each side is ½ m; cut the wire into 2 m (for the square) and 1½ m (for the triangle).
💡 One letter is enough

Here one letter does it: side s, 4s + 3s = 7s = 3.5. You could also write two letters (square piece x, triangle piece y): x + y = 3.5 and x/4 = y/3 – but the one-letter way is quicker.

Question 5 · Girls and boys

Q5A class has 4 more girls than boys. One day only 8 boys were absent, and the girls were then twice the boys present. How many girls and boys are there in the class?

Boys b. Girls b + 4. Boys present b − 8, and the girls are 2(b − 8).

🎬 Solution animation
Answer: 20 boys and 24 girls (check: 24 = 20 + 4; boys present 12, and 24 = 2 × 12).

Question 6 · A fraction puzzle

Q6Adding 1 to the numerator of a fraction and simplifying gives ⅓; adding 1 to the denominator gives ¼. What is the fraction?

Numerator x, denominator y. A fraction equal to ⅓ has its denominator 3 times its numerator.

🎬 Solution animation
Answer: 4/15 (check: 5/15 = ⅓ and 4/16 = ¼).

Question 7 · Two investments

Q7A person invested ₹100000 in two schemes, one paying 7% and the other 6% annual interest. After a year the total interest from both was ₹6750. How much was invested in each?

If all ₹100000 earned 6%, the interest would be ₹6000. Every rupee moved to the 7% scheme earns 1 paisa more.

🎬 Solution animation
Answer: ₹75000 at 7% and ₹25000 at 6% (check: 5250 + 1500 = 6750).
🌍 Why this matters

Banks, post-office schemes and loans all work like this: a total amount, two rates, one total interest. The same two-equation idea finds the split.

Question 8 · Speeding up

Q8An object starts with a speed of u metres/second and its speed increases by a metres/second every second, so its speed in the t-th second is u + at. Its speed in the 1st second is 5 m/s and in the 5th second 13 m/s. At what rate does the speed increase each second? What was the starting speed?

Write u + a = 5 and u + 5a = 13. What does the difference tell you?

🎬 Solution animation
Answer: the speed increases by 2 m/s every second, and the starting speed was 3 m/s.

Make your own: total and difference

🎚️ Build a "set the extra aside" puzzle

Questions 1, 2 and 3 are all this puzzle in disguise. The difference must be smaller than the total, or the smaller amount would be negative.

Check yourself

🧭 What these eight questions teach

Next: Section 2 – two equations and the trick of elimination ▶