14. Lakshmi is a cashier in a bank. She has currency notes of denominations
100, 350 and 310, respectively. The ratio of the number of these
notes is 2:3:5. The total cash with Lakshmi is 34,00,000. How many
notes of each denomination does she have?
15. I have a total of 300 in coins of denomination 1,72 and 5. The
number of 2 coins is 3 times the number of 5 coins. The total number of
coins is 160. How many coins of each denomination are with me?
16. The organisers of an essay competition decide that a winner in the
competition gets a prize of 100 and a participant who does not wine
a prize of 25. The total prize money distributed is 3.000 Find
number of winners, if the total number of participants is 63.
Answers
Step-by-step explanation:
14) The ratio of the notes is : 2 : 3 : 5
Let her have 2 * N number of Rs 100 notes, 3 * N number of Rs 50 notes, and 5 * N number of Rs 10 notes respectively.
Then the total value of the currency notes will be:
2 N * Rs 100 + 3 N * Rs 50 + 5 N * Rs 10 = Rs 4, 00, 000
=> 200 N + 150 N + 50 N = Rs 4, 00, 000
=> 400 N = Rs 4, 00, 000
=> N = 1, 000
Hence, There are 2N = 2,000 notes of Rs 100 , 3N = 3,000 notes of Rs 50 and finally , 5 N = 5, 000 notes of Rs 10..
15) Equations with linear expressions in one variable only are
known as linear equations in one variable.
An algebraic equation is an equality involving variables. It
has an equality sign(=). The expression on the left of the equality sign is the
Left Hand Side (LHS). The expression on the right of the equality sign is the
Right Hand Side (RHS).
In an equation the values of the expressions on the LHS and
RHS are equal.
Transposition:
Any term of a equation may be taken from one side to other
with the change in its sign, this does not affect the equality of the statement
. This process is called transposition.
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Solution:
Let the number of ₹ 5 coins
be x.
& the Number of ₹ 2 coins be 3x.
Total number of coins =160
(Given)
Number of ₹ 1 coin = 160 − (Number of coins of ₹
5 and of ₹ 2)
= 160 − (3x + x)
= 160 – 4x
Amount of ₹1 coins = ₹ [1 × (160 − 4x)]
= ₹ (160 − 4x)
Amount of ₹ 2 coins = ₹ (2 × 3x)= ₹ 6x
Amount of ₹ 5 coins = ₹ (5 × x) = ₹ 5x
A.T.Q
Total
amount is ₹ 300 (given)
(160 – 4x) + 6x + 5x = 300
160+2x+5x=300
160 + 7x =
300
Transposing 160 to R.H.S,
7x =
300 – 160
7x =
140
x= 140/7
x = 20
So , the number of coins of
each denominations will be
Number of ₹1 coins = 160 – 4x
= 160 − 4 × 20
= 160 − 80 = 80
Number of ₹ 2 coins = 3x
= 3 × 20 = 60
Number of ₹ 5 coins = x
= 20
Hence,
Number of ₹1 coins = 80
Number of ₹2 coins = 60
Number of ₹5 coins = 20
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Hope this will help you....
16) Winner of a prize = Rs 100 the runner prize amount = Rs 25
Total sum = Rs 3, 000
Let the number of winners be W and the number of runners = 63 - W
3, 000 = W * 100 + (63 - W) 25
= 75 W + 25 * 63
W = 19
HEYA!!
14. ratio given 2:3:5
of 100 350 and 310 respectively
now for total
now for
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