## Exercise 1 E

#### Question 1

**The product of two rational numbers is -26 . If one of the numbers is -3, find the other.**

Sol :

Let x be the other rational number

A.T.Q

⇒x × (-3) = -26

On transposing

⇒

#### Question 2

**Divide the sum of by the reciprocal of **

Sol :

First lets find sum

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L.C.M of 8 and 12 is =2×2×2×3 =24

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⇒..(i)

then lets find reciprocal of

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then reciprocate it ⇒..(ii)

According to question lets divide

From (i) and (ii)

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#### Question 3

**By what rational number should be divided to get ?**

Sol :

According to question

Let x be the number which can divide

and

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On transposing

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Cross multiply

⇒-25×8=15x ×2

⇒-200=30x

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#### Question 4

**The perimeter of isosceles triangle is cm . If one of its equal sides is cm, find the third side.**

Sol :

Note: An isosceles triangle have 2 equal sides and one unequal side

⇒Equal sides are given

⇒and let unequal (third) side is x

⇒Also , perimeter of isosceles triangle is

⇒perimeter of isosceles triangle= sum of all sides of triangle

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On transposing

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L.C.M of 20 and 5 is =2×2×5 =20

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⇒ cm

#### Question 5

**You participate in a km relay run for charity . Your team has 8 people and each person runs the same distance . How many km does each person run ?**

Sol :

Total distance..(i)

Let x distance travel by each person then total distance traveled is 8x..(ii)

From (i) and (ii)

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#### Question 6

**A postcard is cm long and cm wide . Find the area of the postcard .**

Sol :

⇒Post card is in the shape of rectangle

⇒Length

⇒Breadth

⇒Area of rectangle=Length×Breadth

⇒

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⇒ cm^{2}

#### Question 7

**Rhea went to see two one-act plays. With an intermission of hour , the evening lasted hours . The first play was hours long . How long did the second play last ?**

Sol :

According to question

Total time = First play + intermission + Second play

On transposing

L.C.M of 2, 4 and 6 is =2×2×3 =12

hours

#### Question 8

**If of a number exceeds its by 1 , find the number .**

Sol :

According to question

Let the number be x , then

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On transposing

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L.C.M of 7 and 3 is 21

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Cross multiplication

⇒21=x or

⇒x=21

#### Question 9

**Vaibhav cycles km from school to a book store , km more to the grocery store and then km home . Find the total distance cycled by Vaibhav . Is it more or less than 5 km . If more or less , find the difference .**

Sol :

Total Distance cycled = distance of school to bookstore+ distance of bookstore to grocery store+distance of grocery store to home

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L.C.M of 8,2 and 4 is =2×2×2 =8

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#### Question 10

**Concert ticket usually cost per person . For students they are priced at of the normal cost . How much will 6 tickets cost for students ?**

Sol :

Ticket price for student

For 6 students = 6×Cost of single ticket

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