Question

The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, he buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

Answer 1

Given,

• The Coach of a Cricket team buys 7 bats and 6 balls for Rs.3800
• He buys 3 bats and 5 balls for Rs.1750.

To Find,

• Cost of Each bat and each ball .

Solution,

⇒Suppose the Cost of bat be a

And,Suppose the Cost of ball be b

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The Coach of a Cricket team buys 7 bats and 6 balls for Rs.3800.

$\implies \sf{7a + 6b = 3800}$

$\implies \sf{7a = 3800 - 6b}$

$\implies \boxed{\sf{a = \dfrac{3800 - 6b}{7}}}$

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• He buys 3 bats and 5 balls for Rs 1750.

$\implies \sf{3a + 5b = 1750}$

(Now Put the value of a in Second Condition)

$\implies \sf{3(\dfrac{3800 - 6b}{7}) + 5y = 1750}$

$\implies \sf{\dfrac{11400 - 18b}{7} + 5b = 1750}$

$\implies \sf{\dfrac{11400 - 18b + 35b }{7} = 1750}$

$\implies \sf{\dfrac{11400 + 17b}{7} = 1750}$

$\implies \sf{11400 + 17b = 1750 \times 7}$

$\implies \sf{11400 + 17b = 12250}$

$\implies \sf{17b = 12250 - 11400}$

$\implies \sf{17b = 850}$

$\implies \sf{b = \dfrac{850}{17}}$

$\implies \boxed{\sf{b = 50}}$

Now Put the value of b in First Condition :-

$\implies \sf{a = \dfrac{3800 - 6b}{7} }$

$\implies \sf{a = \dfrac{3800 - 6 \times 50}{7}}$

$\implies \sf{a = \dfrac{3800 - 300}{7}}$

$\implies \sf{a = \dfrac{3500}{7}}$

$\implies \sf{a = \dfrac{3500}{7}}$

$\implies \boxed{\sf{a = 500}}$

Therefore,

$\boxed{\bold{\red{Cost \ of \ Each \ Bat = a = Rs.500}}}$

$\boxed{\bold{\red{Cost \ of \ Each \ ball = b = Rs.50}}}$

$\rule{200}2$

Answer 2

Given

Cost price of 7 bats & 6 balls = Rs.3800

Cost price of 3 bats & 5 balls = Rs.1750

To find

Cost of each bat & ball

Solution

Let the cost price of each bat & ball be a & b respectively.

According to 1st case :

⟼ 7a + 6b = 3800 -eq.( l )

According to 2nd case :

⟼ 3a + 5b = 1750 -eq.( ll )

Now multiplying eq.( l ) by 3 & eq.( ll ) by 7 :

➙ 21a + 18b = 11400 -eq.( lv )

➙ 21a + 35b = 12250 -eq.( v )

Now subtracting eq.( v ) from eq.( lv ) :

21a + 18b = 11400

21a + 35b = 12250

(-) (-) (-)

⤐ -17b = - 850

⤐ b = -850/-17

⤐ b = 50

So, cost price of one ball = Rs.50

Now putting this value in eq. ( l )

⤇ 7a + 6(50) = 3800

⤇ 7a + 300 = 3800

⤇ 7a = 3800 - 300

⤇ 7a = 3500

⤇ a = 3500/7

⤇ a = 500

So, cost price of one bat = Rs.500 .

Therefore,

Cost of one bat & ball = Rs.500 & Rs.50 respectively.