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Mathematics

Sanjay runs a computer repair service company. For an HP laptop, he charges ₹ 320 for diagnosis and ₹ 90 per hour for repairs. For a Dell laptop, he charges ₹ 480 for diagnosis and ₹ 70 per hour for repairs.

(1) Sanjay repairs an HP laptop of Mr Lal. He charges ₹ 950 for the work. How long did the repair work take place?

  1. 6 hours
  2. 7 hours
  3. 8 hours
  4. 9 hours

(2) Sanjay repairs a Dell laptop of Mr Gupta. The total charges were ₹ 830. How long did the repair work take place?

  1. 5 hours
  2. 6 hours
  3. 7 hours
  4. 8 hours

(3) He repairs an HP laptop and a Dell laptop of Mr Subhash. He found that the repair work for both the laptops took equal time and also the service charges of the two laptops were the same. How long did the repair work take place for each laptop ?

  1. 6 hours
  2. 7 hours
  3. 8 hours
  4. 9 hours

(4) What were the total service charges that Mr. Subhash had to pay for both the laptops ?

  1. ₹ 1040
  2. ₹ 1260
  3. ₹ 2040
  4. ₹ 2520

Linear Eqns One Variable

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Answer

Given:

Sanjay's Charge Rates:

HP: ₹ 320 (fixed) + ₹ 90 per hour

Dell: ₹ 480 (fixed) + ₹ 70 per hour

(1)

Let the repair time be x hours.

∴ 320 + 90x = 950

⇒ 90x = 950 - 320 \quad [Transposing +320 to RHS]

⇒ 90x = 630

⇒ x = 7 hours.

Hence, option 2 is the correct option.

(2)

Let the repair time be y hours.

∴ 480 + 70y = 830

⇒ 70y = 830 - 480 \quad [Transposing +480 to RHS]

⇒ 70y = 350

⇒ y = 5 hours.

Hence, option 1 is the correct option.

(3)

Let the time for each be t hours. Since the charges are equal:

HP Charge = Dell Charge

320 + 90t = 480 + 70t

⇒ 90t - 70t = 480 - 320 \quad [Transposing +320 to RHS and +70t to LHS]

⇒ 20t = 160

⇒ t = 16020\dfrac{160}{20}

⇒ t = 8 hours

Hence, option 3 is the correct option.

(4)

Let's calculate the cost for one laptop using t = 8:

HP: ₹ (320 + 90(8)) = ₹ (320 + 720) = ₹ 1040

Dell: ₹ (480 + 70(8)) = ₹ (480 + 560) = ₹ 1040

Total for both (HP + Dell) = ₹ 1040 + ₹ 1040 = ₹ 2080

The total service charges that Mr. Subhash had to pay for both the laptops is ₹ 2080. None of the options are correct.

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