Olympiad Test: Comparing Quantities - Class 8 MCQ

We have A=220 and P=200 for the second year
So A=P(1+R100)1
220=200(1+R100)1
11/10-1=R/100
R=10%

Let x be the marked price

We know

Marked price (Mp)= selling price+discount %of Mp

x=176+20%of x

x=176+0.2x 

x-0.2x=176

0.8x=176

x=176÷0.8

x=220

The marked price is Rs 220

The problem involves finding the principal (sum of money) when the difference between Simple Interest (S.I.) and Compound Interest (C.I.) for 2 years at a rate of 15% p.a. is given as Rs. 144.

Formula for the difference between S.I. and C.I. for 2 years:

Where:

• P = Principal (sum of money to find)
• R = Rate of interest (15%=15/100=0.15)
• Difference = Rs. 144 (given)

Substituting values into the formula:

Final Answer:

The principal (sum of money) is Rs. 6400, which matches Option d).

A = P(1+R/100)t
882 = 800(1+5/100)t
441/400 = (21/20)t
(21/20)2 = (21/20)t
t = 2 years

A = P ( 1 + R/100)^t. Since its half yearly,
t = 2
= 8000 (1 + 5/200)²
= 8405
CI = A-P = 8405 - 8000 = 405

  
⇒ n = 3 years

Population after n years is calculated as:

P_n = P₀ × (1 + r₁) × (1 + r₂) × (1 + r₃)

Where:

• P₀ is the initial population,
• r₁, r₂, r₃ are the growth rates for each year.

Given:

• Initial population P₀ = 25000
• Growth rates:
  • Year 1: 4% = 0.04
  • Year 2: 5% = 0.05
  • Year 3: 8% = 0.08

Now, we can calculate the population after each year:

Year 1:

Population after Year 1 = 25000 × (1 + 0.04) = 25000 × 1.04 = 26000

Year 2:

Population after Year 2 = 26000 × (1 + 0.05) = 26000 × 1.05 = 27300

Year 3:

Population after Year 3 = 27300 × (1 + 0.08) = 27300 × 1.08 = 29484

= Rs.12500

Value of the vehicle after 3 years 

= Rs.89600

 ∴ Total depreciation 

= Rs.(175000−89600)

= Rs.85400

Simple interest for 1 year =400/2=200
CI of 1 year =200
CI for 2nd year=410-200=210
For 2nd year Amount=210 and P=200
A = P (1+R/100)¹
210 = 200(1+R/100)
R=5%

Let the principal be 100x

First year interest = 10% = 10x

Second year interest =10% = 10/100 *110x =11x

Total interest = 21x

If interest is 21x , principal is 100x

If interest is Rs 525 , principal is = 525 /21x *100x = Rs 2500

Simple interest on Rs 2500 at 5% for 4 years is

2500 x 4 x 5/100= Rs500 

CI = A-P
CI = P(1+R/100)²-P
328 = P[(1+5/100)²-1]
328 = P*41/400
P = 3200
SI = 3200*2*5/100 = 320

A woman bought 3 toffees at 25 paise each. So she spent 75 paise and 3 for 65 paise, then totally for 6 toffees she spent Rs.1.40 or for a dozen she spent 

Rs.2.80 and sold the dozen at Rs.3.50. 

∴ Gam

The cost of sugar per kilogram
S.P. = C.P.(1 + gain%) S.P. at 20% profit = Rs.13.95 × 1.2 = Rs.16.74

Gain % = (SP − CP)/CP
Let cost price be Rs. 100.

The MP is Rs. 130.
After discount of 6 1/4 %
the SP is Rs. 130(93.75/100)
= Rs. 121.875
Gain% = [(121.875 - 100)/100]*100
= 21.875​