GSEB Class 6 Maths Solutions Chapter 11 Algebra Exercise 11.4

Question 1. Answer the following:
(a) Take Sarita's present age to be y years
(i) What will be her age 5 years from now?
(ii) What was her age 3 years back?
(iii) Sarita's grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is 2 years younger than grandfather. What is a grandmother's age?
(v) Sarita's father's age is 5years more than 3 times Sarita's age. What is her father's age?
(b) The length of a rectangular hall is 4 metres less than 3 times the breadth of the hall. What is the length, if the breadth is b metres?
(c) A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
(d) Meena, Beena and Leena are climbing the steps to the hilltop. Meena is at step s, Beena is 8 steps ahead and Leena 7 steps behind. Where are Beena and Meena? The total number of steps to the hilltop is 10 less than 4 times what Meena has reached. Express the total number of steps using s.
(e) A bus travels at v km per hour. It is going from Daspur to Beespur. After the bus has moved for 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.
Answer:
(a)
(i) Her age 5 years from now will be \( y + 5 \) years.
(ii) Her age 3 years back was \( y - 3 \) years.
(iii) The grandfather's age is 6 times her age, which is \( 6y \) years.
(iv) The grandmother's age is 2 years younger than the grandfather, making it \( 6y - 2 \) years.
(v) Sarita's father's age is 3 times Sarita's age plus 5 years, which is \( 3y + 5 \) years.
(b) If the breadth of the rectangular hall is \( b \) metres, then its length is \( 3b - 4 \) metres.
(c) If the box has height \( h \) cm, its length is \( 5h \) cm, and its breadth is \( 5h - 10 \) cm.
(d) Meena is at step \( s \). Beena is at step \( s + 8 \), and Leena is at step \( s - 7 \). The total steps to the hilltop can be expressed as \( 4s - 10 \).
(e) The bus travels at \( v \) km/hr. After 5 hours, it travels \( 5v \) km. Since Beespur is 20 km away after 5 hours, the total distance from Daspur to Beespur is \( 5v + 20 \) km.
In simple words: This question asks us to use variables like 'y', 'b', 'h', 's', and 'v' to show ages, lengths, positions, and distances in terms of mathematical expressions. We need to create expressions for each given scenario.

Exam Tip: Remember to clearly define what each variable represents and carefully translate the word problems into algebraic expressions. Pay close attention to keywords like "less than," "times," "more than," "ahead," and "behind" to ensure correct mathematical operations.

Question 2. Change the following statements using expressions into statements in ordinary language. (For example, given Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language - Nalin scores 15 runs more than Salim.)
(a) A notebook costs Rs \( p \). A book costs Rs \( 3p \).
(b) Tony puts \( q \) marbles on the table. He has \( 8q \) marbles in his box.
(c) Our class has \( n \) students. The school has \( 20n \) students.
(d) Jaggu is \( z \) years old. His uncle is \( 4z \) years old and his aunt is \( 4z - 3 \) years old.
(e) In an arrangement of dots there are \( r \) rows. Each row contains 5 dots.
Answer:
(a) A book's price is 3 times the cost of a notebook.
(b) Tony's box contains 8 times the quantity of marbles present on the table.
(c) The school's total number of students is 20 times the count in our class.
(d) Jaggu's uncle is 4 times older than Jaggu, and Jaggu's aunt is 3 years younger than his uncle.
(e) The total number of dots in an arrangement is 5 times the number of rows.
In simple words: We are converting algebraic expressions back into regular sentences. We describe the relationship between quantities using words like "times," "more than," or "less than" instead of symbols.

Exam Tip: Practice converting expressions to words and vice-versa. Focus on phrases that describe multiplication, addition, and subtraction accurately, such as "a multiple of," "increased by," or "decreased by."

Question 3. (a) Given Munnu's age to be \( x \) years, can you guess what \( x - 2 \) may show? Hint: Think of Munnu's younger brother. Can you guess what \( x + 4 \) may show? What \( 3x + 7 \) may show?
(b) Given Sara's age today to be \( y \) years. Think of her age in the future or in the past. What will the following expression indicate?
\( y + 7, y - 3, y + 4\frac { 1 }{ 2 }, y - 2\frac { 1 }{ 2 } \).
(c) Given \( n \) students in the class like football, what may \( 2n \) show? What may \( \frac { n }{ 2 } \) show? Hint: Think of games other than football
Answer:
(a) \( x - 2 \) represents Munnu's younger sister's age, which is 2 years less than his age. \( x + 4 \) shows Munnu's elder brother's age, which is 4 years more than his age. \( 3x + 7 \) indicates Munnu's mother's age, which is 7 years more than 3 times his age.
(b)
(i) \( y + 7 \) shows Sara's age after 7 years.
(ii) \( y - 3 \) indicates Sara's age 3 years ago.
(iii) \( y + 4\frac { 1 }{ 2 } \) represents Sara's age after \( 4\frac { 1 }{ 2 } \) years.
(iv) \( y - 2\frac { 1 }{ 2 } \) shows Sara's age \( 2\frac { 1 }{ 2 } \) years ago.
(c) If \( n \) students in the class like football, then \( 2n \) may represent twice the number of football players, possibly those who like cricket. \( \frac { n }{ 2 } \) could show half the number of football players, perhaps those who like hockey.
In simple words: We are interpreting what various algebraic expressions mean in real-world situations. For ages, plus means older/future, minus means younger/past. For group sizes, multiplying means more of something, and dividing means a fraction of it.

Exam Tip: When interpreting expressions, consider the context given. For age problems, addition means future age or older, and subtraction means past age or younger. For quantities, multiplication suggests multiples, and division suggests fractions or parts.