Practice30Create account

Nisha's marks in Mathematics and Science add up to 90. If she had scored 5 marks more in Mathematics and 5 marks fewer in Science, her Mathematics marks would have been twice her Science marks. How many marks did she score in Science?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A35
  • B55
  • C45
  • D30

Step-by-Step Solution

Let Mathematics = and Science = . Then and → . Substituting: → → and . Check: 55 + 35 = 90 ✓ and ✓. Answering 55 gives the Mathematics marks, and 45 assumes the two subjects were equal, which ignores the second condition entirely.
Answer: A) 35

Key idea: Word problems and translation

Most Class 10 questions on this topic are word problems. The skill is in TRANSLATION:

1. Identify the two unknowns; assign variables (e.g., let = age of A, = age of B).
2. Write two equations from the two given pieces of information.
3. Solve by your preferred method.

**Common types**:
- **Age problems**: 'Father is twice as old as son. Five years ago father was three times. Find ages.'
- **Number problems**: 'A two-digit number plus its reverse is 99...'
- **Distance/time/speed**: 'Boat in still water speeds, downstream/upstream rates...'
- **Cost problems**: 'Cost of pencils and pens.'
- **Fraction problems**: 'A fraction becomes 1/2 when 1 is added to numerator and 2 is subtracted from denominator...'

Always CHECK by substituting solution back into the original word problem (not just the equations).

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Pair of Linear Equations in Two Variables practice questions

More Class 10 Pair of Linear Equations in Two Variables practice

Lines ℓ₁ and ℓ₂ are the graphs of a pair of linear equations in x and y (1 square = 1…Meera plotted both equations of a pair on the same grid and got lines ℓ₁ and ℓ₂ shown.…Kabir drew 2x − y = 2 (thick blue line) and 4x − 2y = 4 (dashed orange line) on the same…The lines x − y + 1 = 0 and 3x + 2y − 12 = 0 are drawn on the grid (1 square = 1 unit).…Lines ℓ₁ and ℓ₂ and the x-axis enclose the shaded triangle. Using the grid (1 square = 1…