Digits, Interest, Ages & Speeds അക്കങ്ങൾ, പലിശ, പ്രായം, വേഗം
Some practice questions use special kinds of quantities: two-digit numbers and their digits, interest on money, people's ages, speeds that keep increasing, the angles of a triangle and remainders after division. Each has one small formula. Learn the six formulas here and those questions become ordinary pairs of equations.
- Writing sentences as expressions and equations; solving one equation by the balance.
- Percent means "out of 100": 7% = 7/100 = 0.07.
1. Two-digit numbers: 10a + b
In 47 the tens digit (പത്തിന്റെ സ്ഥാനം) is 4 and the units digit is 7: 47 = 10 × 4 + 7. A number with digits a and b is 10a + b; with the digits reversed it is 10b + a. The reversed minus the original is 9b − 9a = 9(b − a).
2. Percentage and simple interest for a year പലിശ
At 7% a year, ₹x earns 7/100 of x = 0.07x in one year. If ₹100000 is split into x at 7% and the rest, 100000 − x, at 6%, the total interest is 0.07x + 0.06(100000 − x).
Practice set 1 Q7 asks which split gives ₹6750 interest. Slide until the total reads 6750.
3. Ages: the difference never changes പ്രായം
If someone is x years old now, n years ago they were x − n and n years later they will be x + n. Two people both get older by the same amount, so the difference of their ages stays the same forever.
4. Speed that grows steadily: u + at വേഗം
An object starts with speed u metres per second and gains a metres per second every second. Its speed in the t-th second is u + at, and the distance covered in t seconds is ut + ½at². (u, a are two unknowns – perfect for a pair of equations.)
5. Angles of a triangle
The three angles of any triangle add up to 180°. In a right triangle one angle is 90°, so the other two add up to 90°.
6. Division with remainder
14 ÷ 6 gives quotient 2 and remainder 2, because 14 = 6 × 2 + 2. In general: dividend = divisor × quotient + remainder (the remainder is smaller than the divisor).
- Two-digit number 10a + b; reversed 10b + a; difference 9(b − a).
- Interest for one year at r%: (r/100) × amount.
- Age n years ago x − n, n years later x + n; age differences never change.
- Speed in the t-th second u + at; distance in t seconds ut + ½at².
- Triangle angles add to 180°; the two smaller angles of a right triangle add to 90°.
- Dividend = divisor × quotient + remainder.
Banks use r/100 × amount every day; cars and trains speed up steadily so u + at describes them; your age difference with a sibling is the same today as on the day they were born. Digit puzzles are the basis of check-digits on barcodes and bank cards.
7. Check yourself
These six formulas turn the "special" practice questions into ordinary equations: digits (10a + b), interest (0.07x), ages (x ± n), speeds (u + at, ut + ½at²), triangle angles (180°, 90°) and remainders (dividend = divisor × quotient + remainder).