Finding the pre-sale price of a fridge, a 36-instalment payment, dividing Rs. 600 among three people, and correcting five jumbled spellings

Understanding the topic

Question 6 tests reverse-percentage work, instalment arithmetic, a three-way share written as equal expressions, and word building. In every money part the trap is the same: the discounted or taxed figure is a percentage of the original, so divide rather than add the percentage back.

(a) In an annual sale, Saima buys a Fridge and a Freezer. The sale offers 15% off everything and she pays a total of Rs. 57,120/-. If the price of a freezer, before the sale, is Rs. 40,000/-, what was the price of the Fridge before the sale?

Given: the fridge and freezer together sold for Rs. 57,120 after a 15% discount, and the freezer's price before the sale was Rs. 40,000.

Method: a 15% discount means the buyer pays 85% of the original combined price, so the original price is the sale price divided by 0.85.

Working:

57,120 ÷ 0.85 = 67,200

67,200 - 40,000 = 27,200

Answer: the price of the fridge before the sale was Rs. 27,200.

Check: 15% of 67,200 = 10,080, and 67,200 - 10,080 = 57,120.

(b) Mr. Rasheed pays a deposit of Rs. 60,000/- followed by 36 equal monthly payments. The total amount that he pays is 127% of the basic price of Rs. 3,360,000/-. Calculate Rasheed's monthly payment.

Given: a basic price of Rs. 3,360,000, a total payable of 127% of that price, a deposit of Rs. 60,000, and 36 monthly instalments.

Method: total payable = 1.27 × basic price; subtract the deposit; divide the balance by 36.

Working:

1.27 × 3,360,000 = 4,267,200

4,267,200 - 60,000 = 4,207,200

4,207,200 ÷ 36 = 116,866.666...

Answer: Rasheed's monthly payment is approximately Rs. 116,866.67, or Rs. 116,867 to the nearest rupee.

Check: 36 × 116,866.67 is approximately Rs. 4,207,200, and adding the Rs. 60,000 deposit gives Rs. 4,267,200.

(c) Divide Rs. 600/- among A, B, and C so that Rs. 40 more than 2/5 of A's share, Rs. 20 more than 2/7 of B's share, and Rs. 10 more than 9/17 of C's share may be equal.

Given: A + B + C = 600, and the three expressions (2/5)A + 40, (2/7)B + 20 and (9/17)C + 10 are all equal.

Method: set the three equal expressions to a single value k, make A, B and C the subject, substitute into the total and solve for k.

Working:

(2/5)A + 40 = (2/7)B + 20 = (9/17)C + 10 = k

A = (5/2)(k - 40), B = (7/2)(k - 20), C = (17/9)(k - 10)

(5/2)(k - 40) + (7/2)(k - 20) + (17/9)(k - 10) = 600

Multiplying every term by 18 clears the denominators:

45(k - 40) + 63(k - 20) + 34(k - 10) = 10,800

142k - 3,400 = 10,800

142k = 14,200, so k = 100

A = (5/2)(60) = 150, B = (7/2)(80) = 280, C = (17/9)(90) = 170

Answer: A receives Rs. 150, B receives Rs. 280, and C receives Rs. 170.

Check: 60 + 40 = 80 + 20 = 90 + 10 = 100, and 150 + 280 + 170 = 600.

(d) Find out the correct words from the jumbled spellings given below:

Method: rebuild each word using every supplied letter exactly once, checking the letter count before committing to an answer.

Answers:

1. TEANAIRM is MARINATE
2. VAGNACEXETRA is EXTRAVAGANCE
3. VADIETLIONC is VALEDICTION
4. PKUNYBARTC is BANKRUPTCY
5. TAESRONSC is ANCESTORS

Each answer uses every supplied letter exactly once, which is the check to run before writing a word down.