Question

7. Divide 4000 among A, B and C, so that
their shares may be in the ratio of 5:7:8​

Answer 1

Answer:

Answer:

A's share = ₹1000

B's share = ₹1400

C's share = ₹1600

Step-by-step explanation:

Given :

Total money = ₹4,000

Divide money in the ratio of A,B,C = 5:7:8

To find :

The share between A , B and C

Taken :

Let the A , B , C share be x

So , to find the share between A,B,C use this formula -:

\boxed{\sf{5x+7x+8x=Rs.4000}}

5x+7x+8x=Rs.4000

After finding the value of x multiply with the ratio to find the A , B and C 's share .

Solution :

:\implies\sf{5x+7x+8x=Rs.4000}:⟹5x+7x+8x=Rs.4000

:\implies\sf{20x=Rs.4000}:⟹20x=Rs.4000

:\implies\sf{x=\cancel{\dfrac{Rs.4000}{20}}}:⟹x=

20

Rs.4000

:\implies\sf{x=Rs.200}:⟹x=Rs.200

A's share -:

:\implies\sf{Rs.200\times5}:⟹Rs.200×5

:\implies\sf{Rs.1000}:⟹Rs.1000

B's share -:

:\implies\sf{Rs.200\times7}:⟹Rs.200×7

:\implies\sf{Rs.1400}:⟹Rs.1400

C's share -:

:\implies\sf{Rs.200\times8}:⟹Rs.200×8

:\implies\sf{Rs.1600}:⟹Rs.1600

100% correct answer

Hope it's helpful ✌️✌️

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Answer 2

★ How to do :-

Here, we are given with the total amount that should be divided between three members, namely A B and C. The ratio is also given in which each should get a share out of it. The ratio is given as 5:7:8. The A's share is written in the ratio in the form of 5. The B's share is written in the ratio in the form of 7. The C's share is written in ratio in the form of 8. We are asked to find the amount that each child will get. So, let's solve the problem with explanation.

$\:$

➤ Solution :-

${\tt \leadsto 5:7:8 = 4000}$

For each part of the ratio, insert a variable 'x'.

${\tt \leadsto 5x + 7x + 8x = 4000}$

We can observe that all the numbers have a same variable, so add them up together.

${\tt \leadsto 20x = 4000}$

Shift the number 20 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{4000}{20}}$

Write the fraction in lowest form by cancellation method to get the answer.

${\tt \leadsto x = 200}$

$\:$

We have finally found the value of the variable 'x', so multiply the part of ratio by 'x'

Shares of A :-

${\tt \leadsto 5x = 5 \times 200}$

${\tt \leadsto \boxed{\tt \pink{Rs \: \: 1000}}}$

Shares of B :-

${\tt \leadsto 7x = 7 \times 200}$

${\tt \leadsto \boxed{\tt \pink{Rs \: \: 1400}}}$

Shares of C :-

${\tt \leadsto 8x = 8 \times 200}$

${\tt \leadsto \boxed{\tt \pink{Rs \: \: 1600}}}$

$\:$

Now, let's verify the statement. To verify we can do this, if the sum of the amount received by all students should equal to the total amount.

Verification :-

${\tt \leadsto 1000 + 1400 + 1600 = 4000}$

Add all the values in LHS.

${\tt \leadsto 4000 = 4000}$

${\tt \leadsto LHS = RHS }$

Hence solved !!