Answer the following questions
The ratio of prices of two cars was 3 :
4, three years later, when the price of first had risen by 10% and that of the
second by ₹ 7,000, the
ratio becomes 11 : 15. Find the new prices of the cars.
Answer:
Let the two cars be C1 and C2.
By question,
C1/C2=3/4
Or, 4C1=3C2......(1)
After 3 years,
(C1+10% of C1)/(C2+7000)=11/15
Or, 15{C1+0.1C1}=11(C2+7000)
Or, 15×(1.1)C1=11C2+77000
Or, 16.5C1-11C2=77000.........(2)
Or, 16.5×(3/4)C2-11C2=77000
Or, 12.375C2-11C2=77000
Or, 1.375C2=77000
Or, C2=77000/1.375=Rs56000
Now, C1=(3C2)/4=(3×56000)/4
=Rs42000
Rs 42000 for 1st car
& Rs 56000 for 2nd car
Rohit purchased 200 toys at ₹ 20 each. He sold all toys at ₹ 30 each. Find out total profit and
percentage of profit earned
Answer:
Find the total cost price:
200 x 20 = Rs 4000
Find the total selling price:
200 x 30 = Rs 6000
Find the total profit:
Rs 6000 - Rs 4000 = Rs 2000
Find the profit percentage:
Profit Percentage = 2000/4000 x 100
= 50%
Answer: The profit is Rs 2000 and the
profit percentage is 50%
A person invested some
amount of losses 10% from first year but next year he gains 20% what you had in
the end of the first year if the in there is increase of rupees 1440 in his
capital at the end of 2 years find its original capital
Answer:
18000
Step-by-step explanation:
Suppose you have 100 rs
at the end of 1st year - loss = 10%
remaining amount = 100-100*10%
=90
from question,
2nd year he gains 20% of the remaing amount=
90+90*20%
= 108
from question profit = 1440rs
hence, 108-100= 1440rs
=> 8= 1440 rs
=> 1 = 180 rs
hence => original capital we take = 100
hence original capital = 100*180=18000 Rs
Ans.
A man purchases eggs
at ₹ 65 per dozen and sells them at ₹ 7 per
egg. Find his gain or loss percent.
Answer:
cost price of 1 dozen
(12) egg = ₹65
selling price of 1 egg = ₹7
selling price of 12 egg = 7×12=₹84
since selling price is grater than cost price
therefore there is profit
profit%= S.P.-C.P./C.P. × 100
= 84-65/65×100
=19/65×100
=29.23%
Find the rate of simple interest, if
the sum of money triple itself in 14 years.
Answer
:
Rate of interest = 16%
Explanation:
Method 1:
Formula: RT= (n-1)*100 where
R represents rate of interest, T represents time period and n represents the
number of times it becomes itself.
Here, T = 14 years and n= 3 ( since it
triples itself) [As per the given data}
Substituting all the values in the
formula,
R *14 = (3-1)*100
R*14 = 2*100
R*14 = 200
R = 200/14
R = 16%
Method 2:
Formula : R = (SI *100) / PT (using
basic formula of SI, SI = PTR /100 )
Assume, Principal (P) = 100; Time
period (T) = 14 years; Simple Interest (SI) =200 ( The sum gets tripled so
the value that we assumed 100 becomes 300 which include principal 100 +
interest 200).
Substituting all the values in the
formula we get,
R = (200*100) / 100*14
R = 200/14
R = 16%
The rate of interest at which the money
triples itself is 16%
A Refrigerator set was bought for ₹ 14,000 and sold for ₹ 16,400 through a broker who
charges commission 4% on purchase and 5% on sales. Find the total gain or the
loss in the transaction.
Answer :
The total gain would be Rs. 1700.
Step-by-step explanation:
Since we have given that
Cost price of refrigerator = Rs. 14000
Selling price of refrigerator Rs. 16400
5% commission on purchased price = 0.05
x 14000 700
So, Total purchased price would be
14000+700 = 14700
So, Sp> Cp, there will be profit.
Profit SP-CP
Profit 16400-14700
Profit=1700
Hence, the total gain would be Rs. 1700
The ratio of salaries of Jagriti and
Pravin is 6 : 7 while the ratio of salaries of Pravin and Nilesh 3 : 5. Find
the ratio of salaries of A, B and C. If the salary of Nilesh is ₹ 17,500. Find salary of Jagriti.
Answer :
The ratio of salaries of Jagriti and
Pravin is 6 : 7
the salary of Nilesh is ₹ 17,500.
let the salary of Jagriti = x
ACCORDING TO THE QUESTION
6 : 7= x/17,500
x=20,416.66
the salary of Jagriti =20,146
What is transportation problem ?
Explain the method to solve by North-West corner method.
Answer :
Steps in North West Corner Rule
Select the upper left-hand corner cell
of the transportation table and allocate as many units as possible equal to the
minimum between available supply and demand, i.e., min(s1, d1).
Adjust the supply and demand numbers in
the respective rows and columns.
If the demand for the first cell is
satisfied, then move horizontally to the next cell in the second column.
If the supply for the first row is
exhausted, then move down to the first cell in the second row.
If for any cell, supply equals demand,
then the next allocation can be made in cell either in the next row or column.
Continue the process until all supply
and demand values are exhausted.
Explain the following terms :
· Simple interest is
calculated on the principal,
or original, amount of a loan.
· Compound interest is calculated on
the principal amount and the accumulated interest of previous periods, and thus
can be regarded as “interest on interest.”
· Trade Discount. A
trade discount is the amount by which a manufacturer reduces the retail
price of a product when it sells to a reseller, rather than to the end customer
A
dealer purchased two machines for Rs. 22,000. He sold one of them at a gain of
5% and the other at a loss of 5%. He found that he has neither gain nor loss in
the total transaction. Find C.P. of the machines.
Answer:
The cost price of the first machine is
rs 10000 and the cost price of the second machine is rs 12000.
Step-by-step explanation:
Suppose, the cost of first machine=x
and the cost of second machine=22000-x
Selling price of first machine= x+6%x=
106x/100
Selling price of second machine= y-5%y=
95(22000-x)/100
Selling price of both machine=
106x/100+95(22000-x)/100
= (106x-95x+2090000)/100
= (11x+2090000)/100
According to the question, He has
neither gain nor loss in total transaction.
It means
Cost price of both machine= Sell price
of both machine
22000= (11x+2090000)/100
2200000= 11x+2090000
11x= 2200000-2090000
x= 110000/11
x= 10000
So, y= 22000-10000
y= 12000
Direct proportion
Direct proportion or direct variation
is the relation between two quantities where the ratio of the two is equal
to a constant value.
Marked price.
The price on the label of an
article/product is called the marked price or list price. This is the
price at which product is intended to be sold. However, there can be some
discount given on this price and the actual selling price of the product may be
less than the marked price. It is generally denoted by MP.
What is Singular Matrix?
A square matrix (m = n) that is not
invertible is called singular or degenerate. A square matrix is singular
if and only if its determinant is 0
The transpose of a matrix
is found by interchanging its rows
into columns or columns into rows. The transpose of the matrix is denoted by
using the letter “T” in the superscript of the given matrix. For example, if
“A” is the given matrix, then the transpose of the matrix is represented by A'
or AT.
What is concept inverse of a matrix?
Like numbers, matrices do have
reciprocals. In case of matrices, this reciprocal is called inverse
matrix. If A is a square matrix and B is
its inverse, then the product of two matrices is equal to the unit matrix.
Feasible solution
A feasible solution
is one that satisfies all defined constraints and requirements. A
solution is infeasible when no combination of decision variable values can
satisfy the entire set of requirements and constraints.
Scalar matrix
A scalar matrix
is a type of diagonal matrix. The diagonal elements of the scalar
matrix are equal or same. If the elements of the scalar matrix are all equal to
1, then it becomes an identity matrix. A square matrix A = [aij]n
x n, is said to be a scalar matrix if; aij = 0, when i ≠
j.
The difference between the simple and
compound interest at 15% p.a. on Rs. 1,000, for 3 years.
Answer:
Compound interest :
P = rs 1000 , n =3 , R = 5%
A = P (1+R/100)^n
A = 1000(1.05)^3
A = 1000*1.15763 = Rs 1157.63
Compound interest = Rs 157. 63
Simple interest :
I = PNR /100
I = (1000*3*5/100) = Rs 150
Difference = Rs 7.63
A student finishes a book by reading 30
pages per day in 16 days. If he wants to finish the book in 12 days, how many
pages should be read every day?
Answer:
Total pages in the book = 480 pages
Total time is taken by him to finish
reading the same book = 12 days.
then,
Total pages he should read everyday =
Total pages in the book / Total time taken by him to finish reading the same
book
Total pages he should read everyday =
480/12
Total pages he should read everyday
= 40 pages
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