Question

In a certain T20 Match, a batsman hit only boundaries and sixes for all balls he faced. Total runs he got is 88. The number of shots he hit is 18.

i)By taking number of boundaries he hit as "x" and number of sixes he hit as "y",build up two simultaneous equations ii)Solve the equation and find the number of boundaries and the numbers of sixes it.

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a batsman scored 88 runs only by hitting boundaries and sixes
• Number of shots by batsman is 18

To Find:

• We have to find the number of boundaries and sixes

Concept Used:

The Question can be solved by using the concept of linear equation in two variables which can be further solved by using any of the following techniques

• Substitution
• Elimination
• Cross Multiplication

Solution:

Let the number of boundaries = x

Number of sixes = y

$\odot \:$According to first condition :

The Batsman hit only boundaries and sixes for all balls he faced

The Batsman faced total 18 Balls

$\implies \sf{x + y = 18 }$

$\implies \boxed{\sf{x = 18 - y}}$--------------------------(1)

$\sf{ }$

$\odot \:$According to second condition :

Batsman only hit sixes and boundaries

• Runs scored by sixes = 6y
• Runs scored by boundaries = 4x

Total runs scored by Batman is 88

$\implies \boxed{\sf{Total \: Runs = 88}}$

$\implies \sf{6y + 4x = 88}$

$\implies \sf{3y + 2x = 44 }$

Putting value of x from Equation (1)

$\implies \sf{3y + 2 \: (18-y) = 44 }$

$\implies \sf{3y + 36 - 2y = 44 }$

$\implies \sf{3y - 2y = 44 - 36}$

$\implies \boxed{\sf{y = 8 }}$

$\sf{ }$

Putting value of y in Equation (1)

$\implies \sf{x = 18 - 8}$

$\implies \boxed{\sf{x = 10}}$

_______________________________

$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Number \: of \: Boundaries = 10}}$

$\large\boxed{\sf{Number \: of \: Sixes = 8}}$

_______________________________

$\huge\mathtt\green{Verification:}$

Runs scored by Batsman by hitting only boundaries and sixes is 88

• Runs by sixes = 6 x 8 = 48
• Runs by boundaries = 10 x 4 = 40

➡️ Total Runs = Runs by sixes + Runs by Boundaries

➡️ Total Runs = 48 + 40

➡️ $\boxed{\sf{Total \: Runs = 88}}$

Hence Verified ......

Answer 2

Answer:

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