Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 8 Comparing Quantities Questions Solution. In this chapter, there is total 50 math problems. We have given each questions solution step by step.
1.) Find , if , , , are in proportion.
ANSWER:
Given, , , , are in proportion.
We know,
Four numbers are in proportion then,
First Number x Last Number = Second Number x Third Number
4 x = 6 x 6
= 36 / 4
= 9
2.) Convert 7:8 into percentage.
ANSWER:
We have to convert 7:8 into percentage.
We have to make denominator 100.
We multiply both numerator and denominator by 12.5 to make 100
7 x 12.5 / 8 x 12.5
= 87.5 / 100
7:8 = 87.5%
3.) If % = % , find .
ANSWER:
Given, % = %
We have to find .
% x = % x
= % x / %
= 500
4.) Out of Rs.750, I saved 20%. Find my spending.
ANSWER:
There are total Rs.750. which is 100%
I saved 20%.
My spending = 100% – 20% = 80%.
750 x 80/100
My spending = Rs. 600
5.) In a gathering 87(/) % people are standing. Find the percentage of people not standing.
ANSWER:
There are total 100% people in gathering.
87(/) % people are standing
We have to find people not standing.
People not standing = 100% – 87(/) %
People not standing = 12.5%
6.) Express 12.5% as a ratio.
ANSWER:
We have to express 12.5% as a ratio.
We know,
% is 1/100
12.5% = 12.5 / 100
12.5% = 1/8
7.) Find , if % = .
ANSWER:
% = .
X/100 x 24 = .
X/100 = 144 / 24
X/100 = 6
X = 6 x 100
X = 600
8.) If 25% of a number is 148, find the number.
ANSWER:
Given, 25% of a number is 148
Let, the number is x.
X x 25 / 100 = 148
X = 148 x 100 / 25
X = 592
The number is X = 592
9.) Express 1.234% as a decimal.
ANSWER:
We have to express 1.234% as a decimal.
We know,
% is 1/100
1.234 % = 1.234 / 100
1.234% = 0.01234
10.) 105 chocolates are distributed between Pooja and Anupama in the ratio 2:3. How many chocolates will Anupama get?
ANSWER:
There are total 105 chocolates are distributed between Pooja and Anupama in the ratio 2:3.
Let the chocolate are distributed between Pooja and Anupama are 2x and 3x respectively.
2x + 3x = 105
5x = 105
X = 21
Chocolate of anupama = 3x = 21 x 3 = 63
63 chocolates will Anupama get.
11.) Salma bought a car for Rs.50000 and sold it for Rs.60000. Find her profit percent.
ANSWER:
Given, Salma bought a car for Rs.50000
Cost price = Rs.50000
Sold it for Rs.60000.
Selling price = Rs.60000.
= .. −.P
= Rs.60000 – Rs.50000
= Rs.10000
12.) If % + % + = , find the value of .
ANSWER:
We have to find % + % + =
(X / 100 x 150) + 25 / 100 x + =
150x / 100 + 25x/100 + =
175x / 100 = 175
X = 175 x 100 / 175
X = 100
13.) In an examination, a student has to score 40% marks to pass. He gets 65 marks and fails by 15 marks. Find the maximum number of marks.
ANSWER:
a student has to score 40% marks to pass.
He gets 65 marks and fails by 15 marks.
40% marks to pass = 65 marks + fails 15 marks.
40% marks to pass = 80 marks.
We have to find total marks.
40% = 80 marks.
100% =?
By cross multiplication,
80 x 100 / 40 = 200
The maximum number of mark is 200.
14.) 60% of 30 students are good in mathematics, how many are not good in it?
ANSWER:
Given,
60% of 30 students are good in mathematics
We know, there are total 100% 30 students
Students who are not good in mathematics = 100 – 60 = 40%
Students who are not good in mathematics = 30 x 40/100 = 12
Students who are not good in mathematics are 12.
15.) If % = then find y.
ANSWER:
% =
(42 / 100) X y =
y = 84 x 100 /42
y = 200
16.) Find % Rs.1200.
ANSWER:
We have to find % Rs.1200.
(12 / 100) x Rs.1200
= 12 x 12
% Rs.1200 = Rs. 144
17.) A shopkeeper buys a toy for Rs.2500 and sell it for Rs.3000. Find his gain and gain %.
ANSWER:
Given that,
A shopkeeper buys a toy for Rs.2500 and sell it for Rs.3000.
We know,
= .. −.P
= Rs.3000 – Rs.2500
= Rs.500
% gain = ( / C.P) x 100
% gain = 500 / 2500 x 100
% gain = 20%
18.) How much is 2% of 300 kilogram?
ANSWER:
We have to find 2% of 300 kilogram
We know, % = 1/100
(2/100) x 300
2% of 300 kilogram = 6 kilogram
19.) Find (% ) − (% ).
ANSWER:
We have to find (% ) − (% ).
We know, % = 1/100
(25/100) x 600 – (20/100) x 450
150 – 90
(% ) − (% ) = 60
20.) Express 174% as a fraction.
ANSWER:
We have to express 174% as a fraction.
We know, % = 1/100
174% = 174 /100
174 /100 = 87/ 50
87/ 50 = 1 (37/50)
174% = 87/ 50 = 1 (37/50)
21.) Convert (. 1 + . ) into percentage.
ANSWER:
First we add (. 1 + . )
(. 1 + . ) = 0.148
Now we have to convert it into percentage.
0.148 x 100 = 14.8 %
22.) Sonam’s present salary is Rs.35000. She gets an increment of 10%, find her new salary.
ANSWER:
Sonam’s present salary is Rs.35000. She gets an increment of 10%.
We have to find her new salary.
Increment she gets = Rs.35000 x 10 / 100
Increment she gets = Rs.3500
Sonam’s new salary = Rs.35000 + Rs.3500
Sonam’s new salary = Rs.38500
23.) Find .% .
ANSWER:
.% .
We know, % = 1/100
3.5 / 100 x 500 = 17.5
.% = 17.5
24.) If 75% of a number is added to 150, the result is the number itself. Find the number.
ANSWER:
Let the number is x.
75/ 100 x X + 150 = X
75x/ 100 + 150 = X
3x / 4 + 150 = X
3x + 600 = 4x
4x – 3x = 600
X = 600
The number is 600
25.) The cost of 6 pens is Rs.72. Find the cost of 9 such pens.
ANSWER:
Given.
The cost of 6 pens is Rs.72
We have to find the cost of 9 such pens.
6 pens = Rs.72
9 pens = ?
By cross multiplication,
The cost of 9 such pens = 72 x 9 / 6
The cost of 9 such pens is Rs. 108
26.) Convert / into percentage.
ANSWER:
/ to convert this into percentage we have to make denominator 100
/ we multiply this by 4
x 4 / x 4 = 56 / 100
/ = 56%
27.) Ramesh got 450 marks out of 500. Find his percentage of marks.
ANSWER:
Ramesh got 450 marks out of 500.
We have to find percentage of marks.
450 / 500 x 100 = 90%
Ramesh got 90% of marks.
28.) Find the difference between a paisa and 1% of a rupee.
ANSWER:
We know,
1 rupee = 100 Paisa
1% of 1 rupee = 1 paisa
The difference between a paisa and 1% of a rupee = 1 paisa – 1 paisa
The difference between a paisa and 1% of a rupee = 0
29.) If % + = 4 then find the value of .
ANSWER:
Given,
% + = 4
We know, % = 1/100
40/100 x + = 4
40 / 100 + = 4
2x / 5 + = 4
2x / 5 = 564 – 180
2x / 5 = 384
X = 384 x 5 / 2
X = 192 x 5
X = 960
30.) What is the resultant discount which is equal to (50%+20%) discount?
ANSWER:
We put x = 50% and y = 20%
Resultant discount = x + y – (xy / 100)
Resultant discount = 50%+20% – [(50% x 20%) / 100]
Resultant discount = 70% – 10%
Resultant discount = 60%
31.) Pushpa bought a shirt for Rs.250, a frock for Rs.350 and a pair of jeans for Rs.650. She paid Rs.1000 for all. How much discount did she get?
ANSWER:
Pushpa bought a shirt for Rs.250, a frock for Rs.350 and a pair of jeans for Rs.650.
Sum of all items she bought = Rs.250 + Rs.350 + Rs.650.
Sum of all items she bought = Rs.1250
She paid Rs.1000 for all.
Discount did she get = Rs.1250 – Rs.1000
Discount did she get is Rs. 250
32.) Evaluate % Rs.5000 + % Rs.1000 − % Rs.6000.
ANSWER:
We have to find % Rs.5000 + % Rs.1000 − % Rs.6000.
We know, % = 1/100
= 90/ 100 x 5000 + 80/100 x 1000 – 25/100 x 6000
= 4500 + 800 – 1500
= 5300 – 1500
% Rs.5000 + % Rs.1000 − % Rs.6000 = Rs.3800
33.) Find the difference between simple interest and compound interest for the sum of Rs.2000 at the rate of 10% p. a. for 2 years.
ANSWER:
We know,
Principal = P, Rate of Interest = R % per annum, Time = T years
Simple Interest = = ×× / 0
Here,
Principal = Rs.2000, Rate of Interest = 10%, Time = 2 years
Simple Interest = = 2000 x 10 x 2 / 100
Simple Interest = Rs.400
We know, 1st year simple interest and compound interest are same.
Compound interest of 2nd year = Rs. 200 + Rs. 200 x 10 / 100 = Rs. 220
Difference between simple interest and compound interest = Rs. 220 – Rs. 200
Difference between simple interest and compound interest = Rs. 20
34.) Find the difference between simple interest and compound interest for the sum of Rs.25700 at the rate of 10% p.a. for 1 year.
ANSWER:
We know,
1st year simple interest and compound interest are same.
Difference between simple interest and compound interest for the sum of Rs.25700 at the rate of 10% p.a. for 1 year is 0.
35.) What percent is 75 minutes of 2 hours?
ANSWER:
We know,
1 hour = 60 minutes
2 hours = 2 x 60 minutes = 120 minutes
We have to find percent =
75 minutes of 2 hours = 75 minutes / 120 minutes
(75 minutes / 120 minutes) x 100 = 62.5%
36.) If an article was sold for Rs.93, after a discount of Rs.23.75. Find its marked price.
ANSWER:
Given,
Article was sold for Rs.93= Selling price = Rs.93
Discount of Rs.23.75.
We have to find marked price.
Marked price = Selling price + Discount.
Marked price =Rs.93 + Rs.23.75.
Marked price = Rs.116.75
37.) The price of a computer is Rs.25000. The sales tax charged is 12%. Find the amount that you will have to pay to buy it.
ANSWER:
The price of a computer is Rs.25000. The sales tax charged is 12%.
Amount total pay = Rs.25000 + (Rs.25000 x 12 / 100)
Amount total pay = Rs.25000 + Rs. 3000
Amount total pay = Rs.28000
38.) The present value of a machine is Rs.1000. Its value depreciates every year by 10%. What will be its value after 2 years?
ANSWER:
Given, the present value of a machine is Rs.1000
Its value depreciates every year by 10%.
We have to find its value after 2 years.
We have to find compound interest.
1000 x 10 / 100 = 100
1000 – 100 = Rs. 900 ……….. Depreciation value after 1st year.
900 x 10 / 100 = 90
Rs. 900 – Rs. 90 = Rs. 810 …………………. Depreciation value after 2nd year.
Total depreciate value of 2 years = Rs. 810
39.) Find the simple interest on Rs.7000 for 3 years at the rate of 10% per annum.
ANSWER:
We know,
Principal = P, Rate of Interest = R % per annum, Time = T years
Simple Interest = = ×× / 0
Here,
Principal = Rs.7000, Rate of Interest = 10%, Time = 3 years
Simple Interest = = 7000 x 10 x 3 / 100
Simple Interest = Rs.2100
40.) By selling a chair for Rs.880, Rohan loses 20%. Find the cost price of the chair.
ANSWER:
By selling a chair for Rs.880, Rohan loses 20%.
We know, cost price of the chair is 100%
Rohan loses 20%.
100% – 20% = 80% which is selling price of the chair.
80% = Rs. 880.
100% = ?
By cross multiplication,
Cost price of the chair = Rs. 1100
41.) Express (.+.) /. as percent.
ANSWER:
(.+.) /.
0.300 / .
0.300 / . = 2
We have to convert in percentage.
2 x 100% = 200 %
42.) Find gain or loss in percentage if CP = Rs.1600 and SP = Rs.1840.
ANSWER:
Given,
CP = Rs.1600 and SP = Rs.1840.
We know,
= .. −.P
= Rs.1840 – Rs.1600
= Rs.240
% gain = ( / C.P) x 100
% gain = 240 / 1600 x 100
% gain = 15%
43.) Amisha gets 70 marks in her exams which is 56% of the total marks. Find the maximum marks.
ANSWER:
Given,
Amisha gets 70 marks in her exams which is 56% of the total marks
70 marks = 56%
? = 100%
By cross multiplication,
Maximum marks = 70 x 100 / 56
Maximum marks = 125 Marks.
44.) Find , if % + % + =
ANSWER:
% + % + =
25 / 100 x + /100 x 45 + =
25/100 + 45 / 100 + =
70/100+ =
70x + 9000 = 100x
100x – 70x = 9000
30x = 9000
X = 9000 / 30
X = 300
45.) An umbrella is sold at Rs. 375, with a loss of 25%. What is its cost price?
ANSWER:
Given,
An umbrella is sold at Rs. 375, with a loss of 25%.
We know, cost price of the umbrella is 100%
Loses 25%.
100% – 25% = 75% which is selling price of theumbrella.
75 % = Rs. 375.
100% = ?
By cross multiplication,
Cost price of the umbrella. = Rs. 500
46.) Find , : ∷:
ANSWER:
We know,
Four numbers are in proportion then,
First Number x Last Number = Second Number x Third Number
x = 16 x 9
2 = 144
= 12
47.) Find % + %
ANSWER:
% + %
(15 / 100) x 300 + (20/100) x 400
45 + 80
% + % = 135
48.) Convert . % into fraction.
ANSWER:
. % into fraction.
We know,
% = 1 / 100
. / 100 = 7 / 800
49.) If 20% of 20% of x = 20, then find x.
ANSWER:
20% of 20% of x = 20,
(20/100) x (20/100) x = 20
400/ 10000 x = 20
= 20 x 10000 / 400
= 500
50.) If 40% of a number is added to the number itself, it becomes 560. Find the number
ANSWER:
40% of a number is added to the number itself, it becomes 560
Let number is x.
40x/ 100 + x = 560
140x/ 100 = 560
140x = 560 x 100
X = (560 x 100) / 140
X = 400