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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 2 years younger than grandfather. What is 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 \( h \mathrm{~cm} \). Its length is 5 times the height and breadth is \( 10 \mathrm{~cm} \) 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 \( v \mathrm{~km} \) perhour. It is going from Daspur to Beespur.After the bus has travelled 5 hours, Beespur is still \( 20 \mathrm{~km} \) away. What is the distance from Daspur to Beespur? Express it using \( v \).
To do:
We have to answer the given questions
Solutions:
(a) Present age of Sarita $=y$ years
(i) Sarita’s age 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 $= 6 \times$ Sarita’s present age
$= 6y$ years
(iv) Grandmother’s age$=$ Granfather’s present age $-$ 2
$= (6y -2)$ years
(v) Father’s age $= 5 + 3 \times$ Sarita’s present age
$= (5 + 3y)$ years
(b) The length of the rectangular hall is 4 meters less than 3 times the breadth of the hall.
Length $l= 3 \times$ Breadth $b- 4$
$l = (3b - 4)$ metres
(c) A rectangular box has height \( h \mathrm{~cm} \). Its length is 5 times the height and breadth is \( 10 \mathrm{~cm} \) less than the length.
Length $= 5 \times$ Height
$l = 5h\ cm$
Breadth $=$ Length $- 10\ cm$
$b = (5h - 10)\ cm$
(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.
The step at which Beena is $=$ Step at which Meena is $+ 8$
$= (s + 8)$
The step at which Leena is $=$ Step at which Meena is $- 7$
$= (s – 7)$
Total number of steps $= 4 \times$ (Step at which Meena is) $- 10$
$= (4s - 10)$
(e) A bus travels at \( v \mathrm{~km} \) perhour. It is going from Daspur to Beespur.After the bus has travelled 5 hours, Beespur is still \( 20 \mathrm{~km} \) away.
Speed of the bus $= v\ km/hr$
Distance travelled in 5 hours $= 5 \times v$
$= 5v\ km$
Total distance travelled between Daspur and Beespur $= (5v + 20)\ km$
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