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Mathematics

Case Study III
Tanusha went to a bank to withdraw money. She asked the cashier to give her ₹ 100 and ₹ 500 rupee notes only. The cashier agreed. Tanusha got x, ₹ 100-rupee notes and y, 500-rupee notes.

Based on this information, answer the following questions.

  1. If Tanusha withdrew ₹ 15,000, then the above information can be represented by the linear equation:
    (a) x + 5y = 150
    (b) 5x + y = 150
    (c) x + 5y + 150 = 0
    (d) x + y = 150

  2. If she got 54 notes in all, then the above information can be represented by the linear equation:
    (a) 100x + 500y = 54
    (b) x + y = 54
    (c) 500x + 100y = 54
    (d) 100x + y = 54

  3. If Tanusha withdraws ₹16 000, then which combination of notes might she get?
    (a) ₹500 notes = 30, ₹100 notes = 20
    (b) ₹500 notes = 25, ₹100 notes = 25
    (c) ₹500 notes = 20, ₹100 notes = 30
    (d) ₹500 notes = 30, ₹100 notes = 10

  4. If she gets twenty 500-rupee notes and twenty-five 100-rupee notes, then the amount she withdraws is:
    (a) ₹10,000
    (b) ₹11,000
    (c) ₹12,000
    (d) ₹12,500

  5. Can Tanusha withdraw ₹10,050 under the given conditions?
    (a) yes
    (b) no
    (c) can’t say anything
    (d) none of these

Linear Equations

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Answer

1. Tanusha got x, ₹ 100-rupee notes and y, 500-rupee notes and withdraws ₹ 15,000.

⇒ 100x + 500y = 15000

⇒ 100(x + 5y) = 15000

⇒ x + 5y = 15000100\dfrac{15000}{100}

⇒ x + 5y = 150.

Hence, Option (a) is the correct option.

2. If she received x number ₹ 100 notes and y number of ₹ 500 notes and total notes are 54.

⇒ x + y = 54

Hence, Option (b) is the correct option.

3. If she withdaws ₹ 16,000 and gets x, ₹ 100 notes and y, 500 notes then.

⇒ 100x + 500y = 16000

⇒ 100(x + 5y) = 16000

⇒ x + 5y = 16000100\dfrac{16000}{100}

⇒ x + 5y = 160.

Substituting y = 30 and x = 10 in L.H.S. of the above equation, we get :

⇒ 10 + 5(30) = 10 + 150 = 160 = R.H.S.

Thus, no. of ₹ 100 notes = 10 and no. of ₹ 500 notes = 30.

Hence, Option (d) is the correct option.

4. Given,

She received 25 number ₹ 100 notes and 20 number of ₹ 500 notes,

Amount withdrawn = 100 × 25 + 500 × 20

= 2,500 + 10,000

= ₹ 12,500.

Hence, Option (d) is the correct option.

5. Let x be the number of ₹100 notes and y be the number of ₹500 notes.

The total amount is 100x + 500y.

Can Tanusha withdraw ₹ 10,050.

This means we need to check if the equation 100x + 500y = 10050 has integer solutions for x and y.

The value of x ₹100 notes is 100x, which is a multiple of 100.

The value of y ₹500 notes is 500y, which is also a multiple of 100.

The sum of these two values, the total amount withdrawn, must also be a multiple of 100.

Since, ₹ 10,050 is not a multiple of 100.

Therefore, it is not possible to form the amount ₹ 10,050 using only ₹ 100 and ₹ 500 notes.

Hence, Option (b) is the correct option.

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