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Linear Equations in One Variable

Short Answer Type

41.

Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

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42.

Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

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43.

A rational number is such that when you multiply it by $5 over 2$ and add $2 over 3$ to the product, you get $negative 7 over 12$ . What is the number?

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Long Answer Type

44.

Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2 : 3 : 5. The total cash with Lakshmi is Rs 4,00,000. How many notes of each denomination does she have?

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45.
I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Let the number of Rs 5 coins = x

∴ The number of Rs 2 coins = 3x

∵ Total number of coins = 160

∴                   Number of Re 1 coins = 160 - 3x - x

                                                 = (160 - 4x)

Now, value of:

                                Rs 5- coins = Rs 5 $cross times$ x = Rs 5x

                                Rs 2-coins = Rs 2 $cross times$ 3x = Rs 6x

                                Rs 1-coins = Rs 1 $cross times$ (160-4x) = Rs (160-4x)

According to the condition, we have

                        5x + 6x + (160 - 4x) = 300

or                          5x + 6x + 160 - 4x = 300

or                                         7x +160 = 300

     Transposing 160 to RHS, we have

                                             7x =300 - 160 =140

     Dividing both sides by 7, we have

                                              $straight x equals 140 over 7 equals 20$

∴ Number of:

                                  Rs 5-coins = 20

                                  Rs 2-coins = 3 $cross times$ 20 =60

                                  Rs 1-coins = 160 - (20 $cross times$ 4) = 80

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Short Answer Type

46.

The organisers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63.

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