Question

An amount of Rs. 2050 is divided among A B&C such that the ratio of shares of A&B is 3:4 and that of B&C is 3:5. The share of C exceeds the share of A by
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Answer 1

Question:

An amount of Rs. 2050 is divided among A,B and C such that ratio of shares of A & B is 3:4 and that of B & C is 3:5. By what amount does the share of B exceeds the share of A ?

Answer:

The share of C exceeds the share of A by ;

Rs. 550 .

Note:

• In a ratio, its first term is called antecedent and the second term is called consequent .

• If the simplest form of two or more ratios are same , then they are said to be equivalent ratios.

• Method to find combined ratio:

Step1 : Find the LCM of consequent of first ratio and antecedent of second ratio.

Step2 : Now make the equivalent ratios of both the given ratios such that the consequent of first ratio and the antecedent of second ratio are equal to the obtained LCM.

Step3 : Now finally combine both the ratios.

Solution:

It is given that ;

A:B = 3:4

B:C = 3:5

Let's find the combined ratio of A:B and B:C

(ie; A:B:C)

Step : 1

Here ,

The consequent (second term) of first ratio

(ie; A:B) is 4.

And the antecedent (first term) of second ratio

(ie; B:C) is 3.

Also , the LCM(4,3) = 4×3 = 12

Step : 2

Try to make the consequent of first ratio and antecedent of second ratio equal to there LCM.

Now,

=> A:B = 3:4

=> A:B = (3×3):(4×3)

=> A:B = 9:12

Also;

=> B:C = 3:5

=> B:C = (3×4):(5×4)

=> B:C = 12:20

Hence,

The obtained equivalent ratios are ;

A:B = 9:12 and B:C = 12:20

Step : 3

Now,

Combine the equivalent ratios A:B = 9:12 and

B:C = 12:20.

Hence,

The combined ratio will be ;

A:B:C = 9:12:20

Now , we have;

A:B:C = 9:12:20.

Thus,

Let the A's share be Rs. 9x

B' share be Rs. 12x

C's share be Rs. 20x .

Now,

According to the question,

The amount of Rs. 2050 is divided among A,B and C.

Thus,

=> A's share + B's share + C's share = 2050

=> 9x + 12x + 20x = 2050

=> 41x = 2050

=> x = 2050/41

=> x = 50

Thus,

A's share = Rs. 9x = Rs. 9•50 = Rs. 450

B's share = Rs. 12x = Rs. 12•50 = Rs. 600

C's share = Rs. 20x = Rs. 20•50 = Rs. 1000

Now,

Difference between A's share and B's share

= Rs. 1000 - Rs. 450

= Rs. 550

Hence,

The share of C exceeds the share of A by ;

Rs. 550 .

Answer 2

${\large\bf{\mid{\overline{\underline{Given:-}}}\mid}}$

• Total amount = 2050 Rs.
• A : B = 3 : 4
• B : C = 3 : 5

$\Large\underline\mathfrak{Question}$

• How much C share is more than A ?

$\Large\underline{\underline{\sf{Solution}:}}$

Lets First combined the ratio :-----

Lets assume we have = a : b and c :d .

their combination ratio will be :----

a : b

c : d

$\pink{\large\boxed{\bold{a×c : b×c : b:d}}}$

Here , a : b = A:B = 3 : 4

b:d = B:C = 3 : 5

so, A:B:C = [ 3×3 : 4×3 : 4×5 ] = 9 : 12 : 20 ...

___________________________________

Now, let their share's be = 9x , 12x and 20x .

→ 9x + 12x + 20x = 2050

→ 41x = 2050

→ x = (2050/41) = 50 ...

and, C share is greater than A by = 20x - 9x = 11x .

putting value of x we get,

→ 11x = 11×50 = 550 ...

$\textbf{hence c share is} \: \red{550} \\ \textbf{ greater than a share...}$