Linear Equation
- In a group of equal number of cows and herdsmen, the number of legs was 28 less than four times the number of heads . The number of herdsmen was
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Suppose the number of cows = a therefore , the number of herdsmen = a
The total number of legs = Legs of cows + Legs of herdsmen ( Cow has 4 legs and herdsmen has 2 legs )
The total number of legs = a x 4 + a x 2 = 4a + 2a = 6a
The total number of heads = Heads of cows + Heads of herdsmen ( Cow has 1 head and herdsmen has also 1 head )
The total number of heads = a + a = 2a
According to question,
The total number of legs was 28 less than four times the number of heads,
Solve the equation.Correct Option: D
Suppose the number of cows = a therefore , the number of herdsmen = a
The total number of legs = Legs of cows + Legs of herdsmen ( Cow has 4 legs and herdsmen has 2 legs )
The total number of legs = a x 4 + a x 2 = 4a + 2a = 6a
The total number of heads = Heads of cows + Heads of herdsmen ( Cow has 1 head and herdsmen has also 1 head )
The total number of heads = a + a = 2a
According to question,
The total number of legs was 28 less than four times the number of heads,
6a = 4 x 2a - 28
⇒ 8a - 28 = 6a
⇒ 8a - 6a = 28
∴ a = 28/2 = 14
- A number when subtracted by 1/7 of itself gives the same value as the sum of all the angles of a triangle. What is the number?
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Let us assume the number be N.
According to question,
A number when subtracted by 1/7 of itself gives the same value as the sum of all the angles of a triangle,
N - N x 1/7 = 180 ( As we know sum of all angels of a triangle is 180 .)
Solve the equation.Correct Option: B
Let us assume the number be N.
According to question,
A number when subtracted by 1/7 of itself gives the same value as the sum of all the angles of a triangle,
N - N x 1/7 = 180 ( As we know sum of all angels of a triangle is 180 .)
⇒ N - N/7 = 180
⇒ (7N - N)/7 = 180
⇒ (7N - N) = 180 x 7
⇒ 6N = 180 x 7
⇒ N = 180 x 7/6
⇒ N = 30 x 7
⇒ N = 210
- A number of two digits has 3 for its unit's place,and the sum of digits is 1/7 of the number itself, The number is
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Let us assume the ten's place digit be x.
Then, the number = 10x + 3
and sum of digits = x + 3
According to question,
So, ( x + 3 ) = 1/7( 10x + 3 )
Solve the equation.Correct Option: C
Let us assume the ten's place digit be x.
Then, the number = 10x + 3
and sum of digits = x + 3
According to question,
So, ( x + 3 ) = 1/7( 10x + 3 )
⇔7x + 21 =10x +3
⇔ 3x = 18
⇔ x = 6
The number = 10x + 3 = 10 x 6 + 3 = 60 + 3 = 63
- 11 friends went to a hotel and decided to pay the bill amount equally, But 10 of them could pay ₹ 60 each, as a result 11th has to pay ₹ 50 extra than his share . Find the amount paid by him?
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Let total bill would be ₹ P
Each one will to pay = ₹ P/11
10 friends could pay 10 x 60 = ₹ 600
According to question
600 + P/11 + 50 = P
Solve the equation.Correct Option: C
Let total bill would be ₹ P
Each one will to pay = ₹ P/11
10 friends could pay 10 x 60 = ₹ 600
According to question
600 + P/11 + 50 = P
⇒ 650 = P - P/11
⇒ 650 = (11P - P)/11
⇒ 650 x 11 = (11P - P)
⇒ 650 x 11 = 10P
⇒ P = 11 x 65
⇒ P = 715
Amount paid by 11th friend = 715/11 + 50 = ₹ 115
- A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black sock is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was :
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Let us assume the number of brown socks = B
Let us assume the price of brown socks = ₹ P per pair
Then price of black socks = ₹ 2P per pair
Before interchanging the shocks the amount = amount of black shocks + amount of brown shocks
⇒ Before interchanging the shocks the total amount = 4 x 2P + B x P
⇒ Before interchanging the shocks the total amount = 8P + BP
After interchanging the shocks the total amount = amount of black shocks + amount of brown shocks
⇒ After interchanging the shocks the total amount = 4 x P + B x 2P
⇒ After interchanging the shocks the total amount = 4P + 2BP
According to question,
After interchanging the shocks the total amount = Before interchanging the shocks the amount + Before interchanging the shocks the amount x 50 %
Solve the Equation.Correct Option: B
Let us assume the number of brown socks = B
Let us assume the price of brown socks = ₹ P per pair
Then price of black socks = ₹ 2P per pair
Before interchanging the shocks the amount = amount of black shocks + amount of brown shocks
⇒ Before interchanging the shocks the total amount = 4 x 2P + B x P
⇒ Before interchanging the shocks the total amount = 8P + BP
After interchanging the shocks the total amount = amount of black shocks + amount of brown shocks
⇒ After interchanging the shocks the total amount = 4 x P + B x 2P
⇒ After interchanging the shocks the total amount = 4P + 2BP
According to question,
After interchanging the shocks the total amount = Before interchanging the shocks the amount + Before interchanging the shocks the amount x 50 %
4P + 2BP = 8P + BP + (8P + BP ) x 50%
⇒ 4P + 2BP = 8P + BP + (8P + BP ) x 50/100
⇒ 4P + 2BP = 8P + BP + (8P + BP ) x 1/2
⇒ 4P + 2BP = ( 16P + 2BP + 8P + BP ) x 1/2
⇒ (4P + 2BP) x 2 = ( 16P + 2BP + 8P + BP )
⇒ 8P + 4BP = 24P + 3BP
⇒ 8P + 4BP = 24P + 3BP
⇒ 4BP - 3BP = 24P - 8P
⇒ BP = 16P
⇒ B = 16
The ratio of the number of black and brown pairs of socks = Number of block shocks / Number of Brown Shocks
⇒ The ratio of the number of black and brown pairs of socks in the original order = 4/16 = 1/4 = 1: 4
