Ex 3.2 Q3 (i) - The difference between two numbers is 26 and one number is three times the other. Find them.

Ex 3.2 Q3 (i) - The difference between two numbers is 26 and one number is three times the other. Find them.

Solution:-

Let,

      Larger number = x

      Smaller number = y

Case (i): The difference between two numbers is 26,

   ∴ x - y = 26

   ∴ x = 26 + y       ------- (i)

Case (ii): One number (larger) is three times the other (smaller),

   ∴ x = 3y

   ∴ 26 + y = 3y       { from (i) }

   ∴ 3y - y = 26

   ∴ 2y = 26

   ∴ y =

26 / 2

   ∴ y = 13

➙ Putting y = 13 in Eqⁿ(i)

   ∴ x = 26 + 13

   ∴ x = 39

Therefore,

      Larger number = x = 39

      Smaller number = y = 13

Hence,

          The required numbers are 39 and 13.

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Try This..

✒ Two numbers add up to 70. The larger number is 4 times the smaller. Find them.

✒ One number is 5 more than twice the other. Their sum is 35. Find the numbers.

✒ The difference between two numbers is 18. One number is twice the other. Find the numbers.

✒ The sum of two numbers is 40. One number is 4 times the other. Find the numbers.

❌ Common Mistakes

Forgetting to define variables properly:

▸ Always start by letting x and y represent clear values.

Ignoring the order of difference:

▸ If the question says "difference is 26", don’t treat it as always positive; clarify which number is bigger.

Mixing up equations:

▸ Keep track of which equation came from which statement.

Skipping verification:

▸ Always check your answer to ensure it satisfies both conditions.

📝 Related Questions:-

• Ex 3.2 Q2 - Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.
• Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
• Ex 3.2 Q3 (iii) - The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.
• Ex 3.2 Q3 (iv) - The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
• Ex 3.2 Q3 (v) - A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
• Ex 3.2 Q3 (vi) - Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Queries Solved:-

Class 10 Ex 3.2

Ex 3.2 Q3 i Class 10

Class 10 Ex 3.2 Q3 i

Class 10 Chap 3 Ex 3.2 Q3 i

Class 10 Pair Of Linear Equations in Two Variables

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