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# 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 two years younger than grandfather. What is the grandmother's age?

(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father’s age?

(b) The length of a rectangular hall is 4 meters less than 3 times the breadth of the hall. What is the length, if the breadth is b meters?

(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 hill top. 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 hill top 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 travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.

**Solution:**

We use the concepts of algebra and the basic of algebra to answer the given questions.

a) Let Sarita’s present age be y years.

(i) Sarita’s age after 5 years from now = Sarita’s present age + 5 = (y + 5) years

(ii) Sarita’s age 3 years back = Sarita’s present age – 3 = (y – 3) years

(iii) Grandfather’s age = 6 × Sarita’s present age = 6y years

(iv) Grandmother’s age = grandfather's present age – 2 = (6y -2) years

(v) Father’s age = 5 + 3 × Sarita’s present age = (5 + 3y) years

(b) We know that the breadth of the rectangular hall is b meters.

Since the length of a rectangular hall is 4 meters less than 3 times the breadth of the hall,

the length = 3b – 4 meters

Therefore, the length of the rectangular hall = 3b - 4 meters

(c) We know that the height of a rectangular box = h cm

Since the length of the rectangular box is 5 times the height, the length = 5 x h cm = 5h cm

Since the breadth of the rectangular box is 10 cm less than the length, the breadth = 5h - 10 cm

Therefore, the length of the rectangular box = 5h cm

The breadth of the rectangular box = 5h – 10 cm

(d) We know that Meena is at step = s

Steps covered by Beena = s + 8

Steps covered by Leena = s – 7

Therefore, Beena is at step s + 8

and, Leena is at step s – 7

The total number of steps to the hill top is 10 less than 4 times what Meena has reached.

Therefore, the total number of steps to the hill top = 4s – 10

(e) We know that the speed of the bus going from Daspur to Beespur = v km/hr

We also know that distance = speed × time

Therefore, distance travelled by the bus in 5 hours =v × 5 km = 5v km

Since Beespur is still 20 km away, the distance between Daspur and Beespur = the distance travelled by the bus in 5hours + 20km = (5v+20) km

Therefore, the distance between Daspur and Beespur = (5v + 20) km

Class 6 Maths NCERT Solutions Chapter 11 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 two years younger than grandfather. What is the grandmothers age?(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her fathers age?(b) The length of a rectangular hall is 4 meters less than 3 times the breadth of the hall. What is the length, if the breadth is b meters?(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 hill top. 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 hill top 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 travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.

**Summary:**

(i) Sarita's age five years from now is (y + 5) years given that Sarita's present age is y years. (ii) Sarita's age 3 years back was (y - 3) years given that Sarita's present age is y years. (iii) Sarita's grandfather's age is 6y years (iv) Sarita's grandmother's age is (6y - 2) years (v) Sarita's father's age is (5 + 3y) years. (b) The length of the rectangular hall is 3b - 4 meters. (c) The length and the breadth of the rectangular box in terms of the height are 5h cm and 5h -10 cm respectively. (d) The total number of steps to the hill top in terms of s is 4s – 10. (e) The distance between Daspur and Beespur in terms of v is (5v + 20) km

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