Chapter 9: Comparing Quantities

Q31Written answer

The discount on an item for sale is calculated on the _________

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Worked solution

Solution: Marked price

Q32Written answer

When principal P is compounded semi-annually at r % per annum for t years, then Amount = ______

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Worked solution

Solution: A = P(1+R/200)^2t

Q33Written answer

Percentages are equal to fractions with _________ equal to 100.

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Solution: Denominator

Q34Written answer

The marked price of an article when it is sold for Rs. 880 after a discount of 12% is ______

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Solution: Rs.1000

Explanation: selling price = Rs.880

Discount percentage = 12%

Let x be the marked price.

Since, discount is calculated on marked price, thus;

x – x × (12/100) = 880

88x /100 = 880

x = 10 × 100 = 1000

Q35Written answer

The compound interest on Rs 8,000 for one year at 16% p.a. compounded half yearly is ______, given that (1.08)² = 1.1664.

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Worked solution

Solution: Rs. 9331.2

Explanation: Principal = Rs.8000

Time period = 1 year

Rate = 16% = 16/100 = 0.16

Amount = P ( 1+r/n)^nt

n = 2 (compounded half yearly in a year)

A = 8000(1+0.16/2)^2×1 = 8000 (1+0.08)² = 8000 (1.08)²

A = 8000 × 1.1664

A = 9331.2

Q36Written answer

In the first year on an investment of Rs. 6,00,000, the loss is 5%, and in the second year, the gain is 10%, the net result is 627000.

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Solution: 627000

Explanation: Investment amount = 600000

Loss in first year = 5%.

So, investment in first year = 600000 – (5/100) x 600000 = 600000 – 30000 = 570000

In second year, the gain is 10%.

So, net result = 570000 + (10/100) x 570000 = 570000 + 57000 = 627000

Q37Written answer

If amount on the principal of Rs 6,000 is written as 6000 [1+5/100]³ and compound interest is payable half yearly, then the rate of interest p.a. is ____ and time in years is ______.

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Solution: Rate – 10% and 1.5 years

Q38Written answer

By selling an article for Rs 1,12,000, a girl gains 40%. The cost price of the article was _______

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Solution: Rs.80000

Explanation: Selling price of the article = ₹112000

Gain% = 40%

Say, x is the cost price of the article.

Since, cost price = selling price – profit % on cost price

Therefore, Selling price = cost price + profit % on cost price

Hence,

112000 = x + x × (40/100)

112000 = x + (2/5)x

112000 = 7x/5

x = (112000 × 5)/7

x = 80000

Q39Written answer

The loss per cent on selling 140 geometry boxes at the loss of S.P. of 10 geometry boxes is equal to _____

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Worked solution

Solution: 20/3%

Explanation: Say, the selling price of one geometry box = Rs.1

So, the selling price of 140 geometry boxes = 1 × 140 = Rs.140

Selling price of 10 geometry boxes = Rs.10

Loss = Rs. 10

Loss percentage = Loss/CP × 100

= 10/(140+10) × 100

= 10/150 × 100

= 20/3%

Q40Written answer

The cost price of 10 tables is equal to the sale price of 5 tables. The profit per cent in this transaction is _____

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Worked solution

Solution: 100%

Explanation: Say, the cost price of one table is Rs.1

Cost price of 10 tables = Sale price of 5 tables (Given)

Sale price of 5 tables profit = cost price of 5 tables = Rs. 5

Profit percentage = Profit/CP × 100

= 5/5 × 100 = 100%

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