question_answer 1)

Answer the following. (a) Take Santa'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 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 time 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 \[\upsilon \] 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.                

Answer:

                (a) Let Santa's present age = y yr (i) Sarita's age after 5 yr from now \[=(y\text{ }+5)\text{ }yr\] (ii) Santa's age 3 yr back \[=(y-3)\text{ }yr\] (iii) Given, Sarita's grandfather is 6 times of her age So, Sarita's grandfather age \[=6\times \] Sarita's present age \[=6\times y=6yyr\] (iv) Given, grandmother is 2 yr younger than grandfather. Age of grandfather = 6y yr        [from (iii)] \[\therefore \] Age of grandmother = [Grandfather's age \[-2\]] yr \[=(6y-2)yr\] (v) Given, Sarita's father's age is 5 yr more than 3 times Sarita's age. Sarita's present age = y yr 3 times of Sarita's age = 3y yr \[\therefore \] Sarita's father age \[=3\times \]  Sarita's age + 5 \[=(3y+5)\,yr\] (b)          Given, the breadth of the hall = b m Now, according to the question, Length of hall = 4 m less than 3 times the breadth of the hall = (3 \[\times \] breadth of hall) ? 4 \[=(3\times b-4)m\] \[=(3b-4)\,m\] Hence, if breadth is b m, then length of hall is \[(3b-4)\,m\]. (c)           Given, the height of a rectangular box = h cm          According to the question, Length of the box = 5 times the height \[=5h\,cm\] and breadth of the box = 10 cm less than the length = 10 cm less than \[5h\] \[=(5h-10)\,cm\] (d)          Given, the Meena is at step = s Also, Beena is 8 steps ahead. \[\therefore \] Beena is at step = s + 8 and Leena is 7 steps behind \[\therefore \] Leena is at step \[=s-7\] Now, total number of steps = 10 less than 4 times Meena's steps \[=4\times \] Meena's steps \[-10=4s-10\] Hence, total number of steps using scan be expressed as \[(4s-10)\]. (e)          Given, speed of the bus \[=\upsilon \,k/h\] i.e. Distance travelled by bus in \[1h=\upsilon \,km\] \[\therefore \] Distance travelled by bus is 5 h from Daspur \[=5\upsilon \,km\] After travelling 5 hours, Beespur is still 20 km away. So, total distance from Daspur to Beespur \[=(5\upsilon +20)\,km\]. Hence, distance from Daspur to Beespur in terms of v can be expressed as \[(5\upsilon +20)km\].