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Olympiad Test: Comparing Quantities


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20 Questions MCQ Test Mathematics (Maths) Class 8 | Olympiad Test: Comparing Quantities

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Olympiad Test: Comparing Quantities - Question 1

A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at the end of first and second years respectively. What is the rate percent?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 1

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%

Olympiad Test: Comparing Quantities - Question 2

The sale price of a shirt is Rs.176. If a discount of 20% is allowed on its marked price, what is the marked price of the shirt?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 2

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

Olympiad Test: Comparing Quantities - Question 3

The difference in S.I. and C.I. on a certain sum of money in 2 years at 15% p.a. is Rs.144. Find the sum.

Detailed Solution for Olympiad Test: Comparing Quantities - Question 3

Let principle be p

T=2years

R=15%

SI= P*R*T/100 

=P*2*15/100 

=3P/10amount for ci

= P(1+R/100) 

=p(1+15/100) 

=529/400pCI=529P/400-P 

= 529-400/400

= 129/400PCI-SI

=144(given)129p/400-3p/10

=144129p-120p/400

=1449p/100=144p

=144*100/9p

=6400Therefore sum

=6400rs

Olympiad Test: Comparing Quantities - Question 4

In what time will a sum of Rs. 800 at 5% p.a. C.I. amount to Rs. 882?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 4

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

Olympiad Test: Comparing Quantities - Question 5

What is the C.I. on Rs. 8000 for 1 year at 5% p.a. payable half-yearly?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 5

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

Olympiad Test: Comparing Quantities - Question 6

Raghu borrowed Rs. 25000 at 20% p.a. compounded half-yearly. What amount of money will clear his debt after 112years?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 6

 

Olympiad Test: Comparing Quantities - Question 7

In what time will Rs.1000 amount to Rs.1331 at 10% p.a. compounded annually?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 7

  
⇒ n = 3 years

Olympiad Test: Comparing Quantities - Question 8

The present population of a town is 25000. It grows at 4%, 5% and 8% during first year, second year and third year respectively. Find the population after 3 years.

Detailed Solution for Olympiad Test: Comparing Quantities - Question 8

Olympiad Test: Comparing Quantities - Question 9

The value of an article which was purchased 2 years ago, depreciates at 12% per annum. If its present value is Rs.9680, what is the price at which it was purchased?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 9



 

= Rs.12500

Olympiad Test: Comparing Quantities - Question 10

The cost of a vehicle is Rs.175000. If its value depreciates at the rate of 20% per annum, find the total depreciation after 3 years.

Detailed Solution for Olympiad Test: Comparing Quantities - Question 10

Value of the vehicle after 3 years 

= Rs.89600

 ∴ Total depreciation 

= Rs.(175000−89600)

= Rs.85400

Olympiad Test: Comparing Quantities - Question 11

The C.I. on a certain sum for 2 years is Rs. 410 and S.I. is Rs. 400. What is the rate of interest per annum?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 11

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%

Olympiad Test: Comparing Quantities - Question 12

The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. Calculate the S.I. on the same sum for double the time at half the rate percent per annum.

Detailed Solution for Olympiad Test: Comparing Quantities - Question 12

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 

Olympiad Test: Comparing Quantities - Question 13

The S.I. on a sum of money for two years is Rs. 660, while C.I. is Rs.696.30, the rate of interest being the same in both the cases. Find the rate of interest.

Detailed Solution for Olympiad Test: Comparing Quantities - Question 13

Olympiad Test: Comparing Quantities - Question 14

A sum of money doubles itself in 3 years at C.I., when the interest is compounded annually. In how many years will it amount to 16 times of itself?

Olympiad Test: Comparing Quantities - Question 15

The C.I. on a certain sum at 5% for 2 years is Rs. 328. Calculate the S.I. for the sum at the same rate and for the same period.

Detailed Solution for Olympiad Test: Comparing Quantities - Question 15

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

Olympiad Test: Comparing Quantities - Question 16

Find the amount on Rs.12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year.

Detailed Solution for Olympiad Test: Comparing Quantities - Question 16

 

Olympiad Test: Comparing Quantities - Question 17

Sugar is bought at Rs.16.20 per kg and sold at Rs.17.28  per kg. What is the gain percent?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 17

Olympiad Test: Comparing Quantities - Question 18

A woman bought two packs of toffees, with the same of number of toffees in each pack. She bought the first pack at 25 paise per toffee and the second pack at 3 toffees for 65 paise. She mixed them together and sold at Rs.3.50 a dozen. What is her gain percent?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 18

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

Olympiad Test: Comparing Quantities - Question 19

A man bought 542 kg of sugar for Rs. 7560.90and sold it so as to gain 20%. What is the selling price per kilogram of sugar?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 19

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

Olympiad Test: Comparing Quantities - Question 20

A trader marks his goods 30% above the cost price but makes a reduction of  on the marked price for ready money. What is his gain percent?

Detailed Solution for Olympiad Test: Comparing Quantities - Question 20

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​    
 

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