Solved Questions on Comparing Quantities
1. The price of sugar has increased by 30%. What percentage of sugar intake needs to be reduced in order to maintain the same amount spent on sugar?
a) 31⁄13%
b) 131⁄13%
c) 231⁄13%
d) 331⁄13%
Answer: c) 231⁄13%
Explanation: Let price of x kg of sugar be $100.
The price of sugar has increased by 30%.
Increase in price of sugar = 30% of $100 = (30/100) × 100 = $30
Increased price = $100 + $30 = $130
Consumption of sugar at $130 = x kg
Sugar intake needs to be reduced in order to maintain the same amount spent on sugar.
Consumption of sugar at $1 = x/130 kg
Consumption of sugar at $100 = (x/130) × 100 = 10x/13
Decrease in consumption = x − 10x/13 = 3x/13
Required % of decrease in consumption = 
2. Shakira bought a washing machine for $956.25 including 12.5% value-added tax. What was the price of the washing machine before value added tax was added?
a) $750
b) $850
c) $950
d) $1050
Answer: b) $850
Explanation: Price of a washing machine including value-added tax = $956.25
Let price of washing machine before value added tax was added be $x.
Value-added tax = 12.5% of Price before value-added tax
= 12.5/100 × x
= $(125x/1000)
Price before value added tax + Value added tax = Price including value added tax
⇒ x + 125x/1000 = 956.25
⇒ (1000x + 125x)/1000 = 95625/100
⇒ 1125x/1000 = 95625/100
⇒ x = [(95625/100) × 1000]/1125
⇒ x = $850
3. A jewellery shop in New York allows a 25% discount on its jewellery and still makes a profit of 25%. What is the marked price of a pair of synthetic ruby earrings that the shopkeeper bought for $500?
a) $833.33
b) $833.66
c) $866.33
d) $866.66
Answer: a) $833.33
Explanation: Cost Price (C.P.) of a pair of earrings = $500
Profit% = 25%
Selling Price (S.P.) of a pair of earrings = [(100 + profit%) ÷ 100] × C.P.
= [(100 + 25) ÷ 100] × 500
= (125 ÷ 100) × 500
= $625 ……………..(1)
Let Marked Price (M.P.) of a pair of earrings be $x.
Discount% = 25%
Selling Price (S.P.) of a pair of earrings = [(100 − Discount%) ÷ 100] × M.P.
= [(100 − 25) ÷ 100] × x
= (75 ÷ 100) × x
= $(75x⁄100) ……………..(2)
From (1) and (2),
75x⁄100 = 625
⇒ x = 625 × 100⁄75
⇒ x = $833.33
Marked price of a pair of synthetic ruby earrings is $833.33.
4. Mr. Bond borrowed $95000 from a bank at 13% per annum in simple interest and an equal sum from another bank at 6% per annum compounded half-yearly. What is the total interest paid to the banks by Mr Bond in a year?
a) $18105.50
b) $18115.50
c) $18125.50
d) $18135.50
Answer: d) $18135.50
Explanation: In case of Simple Interest:
P = $95000
R = 13% p.a
T = 1 year
S.I. = (P × R × T) ÷ 100
= (95000 × 13 × 1) ÷100
= $12350
In case of Compound Interest:
P = $95000
r = 6% p.a (Compounded half yearly)
t = 1 year
C.I. = A − P
= 100785.50 − 95000
= $5785.50
Total interest paid to the banks by Mr. Bond in a year = S.I. + C.I.
= $(12350 + 5785.50)
= $18135.50
5. What is the compound interest on $62500 for 6 months at 8% per annum compounded quarterly?
a) $2512.5
b) $2525
c) $2537.5
d) $2550
Answer: b) $2525
Explanation: P = $62500
r = 8% p.a (Compounded quarterly)
t = 6 months = 6/12 year = ½ year
