CDS Mathematics · Linear Equations

Word Problems

Name each unknown, turn each sentence into one equation, and solve; the arithmetic is simple once the equations are right.

All Linear Equations notes CDS Mathematics strategy

Why this matters

Thirteen PYQs, two of them HARD. Numbers and their digits, fractions, pay with fines, bills with two parts, rows of chairs: each is two sentences and two unknowns. The skill is translating 'is 9 more than four times' exactly.

Concept 1 of 1: From sentences to equations

Every condition in the story is one equation. Choose the unknowns so the equations are as simple as possible — often the quantity the question asks for.

Definition

Two-digit number with digits $a, b$ : $10a + b$ ; digits reversed: $10b + a$ .
'Divided by $S$ gives quotient $q$ , remainder $r$ ': $N = qS + r$ , with $r < S$ .
Paid for days worked, fined for days absent: $pw - f(D - w) = \text{total}$ .
A bill 'partly proportional to rooms, partly to units': $pm + qn$ .
A fixed total rearranged (rows × chairs, pages × lines): the product stays the same.

Reversed digits

(10a + b) - (10b + a) = 9(a - b)

Worked example

A worker is paid Rs.

400

a day worked and fined Rs.

50

a day absent. Over

25

days he receives Rs.

7750

. How many days did he work?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (II) 2021 — Elementary Mathematics · Q42Easy

Example 1 · Linear Equations · Word Problems and Applications

A person agrees to work for 30 days, on a condition that for every day's work he should receive Rs. 500, and that for every day's absence from work he should forfeit Rs. 100. At the end of the time he received Rs. 11,400. How many days did he work ?

The remainder must be smaller than the divisor

'Quotient

6

, remainder

6

' only works when the divisor exceeds

6

. Check each remainder against its divisor before accepting a solution.

Drill 12 more on from sentences to equations

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

From sentences to equations
Reversed digits
$(10a + b) - (10b + a) = 9(a - b)$

Watch out for (1)

The remainder must be smaller than the divisor
→ From sentences to equations

Test yourself on Linear Equations

15 past CDS questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Linear Equations chapter test Drill all 13 questions