Question

A, B and C have Rs.1285/- between them. A’s share is greater than five – sixth of B’s by Rs.25/- and C’s is four – fifteenth of B’s. Find the share of B (in Rs.).

Answer 1

Given:

• Total amount shared by $A,B$ and $C$ =$Rs.1285$.
• Share of '$A$' is greater than $(5/6)B$ by $Rs.25$.
• Share of '$C$' is $(4/15)B$.

To find:

The share of '$B$' in rupees.

• "Share" is the part of amount or any things owned by a person after any division between two or more persons.

Step-wise Solution:

Given that,

$A+B+C=1285$......(1)

The share of '$A$' is given by:

$A=(5/6)B+25$.......(2)

The share of '$C$' is given by:

$C=(4/15)B$.....(3)

The equations $(2)$ and $(3)$ show that, the shares of '$A$' and '$C$' are written in terms of '$B$'.

Substituting the equations ($2$) and ($3$) in equation ($1$), the share of '$B$' can be found. This is done in the following way:

$(5/6)B+25+B+(4/15)B=1285$......(4)

By solving the equation ($4$), the share of '$B$' can be found.

The share of '$B$' is calculated in the following way:

$(5/6)B+B+(4/15)B=1285-25\\((5/6)+1+(4/15))B=1260$

To solve this, find the L.C.M of the denominators '$6$' and '$15$'. The L.C.M for the numbers '$6$' and '$15$' is "$30$".

Now,

$((25+30+8)/30)B=1260\\(63/30)B=1260\\(21/10)B=1260\\B=(1260*10)/21\\B=12600/21\\B=600$

Hence, the share of '$B$' is $Rs.600$.

Now, using equations $(1),(2)$ and $(3)$, the shares of '$A$' and '$C$' can also be found.

Equation (2)⇒

Share of '$A$' = $(5/6)B+25$

$A=((5/6)*600)+25\\A=500+25\\A=525$

∴ The share of '$A$' is $Rs.525$

Equation (3)⇒

Share of '$C$' = $(4/15)B$

$C=(4/15)*600\\C=4*40\\C=160$

∴ The share of '$C$' is $Rs.160$

Final Answer:

The share of '$B$' is $Rs.600$.

Answer 2

Answer:

share of B is Rs 600

Step-by-step explanation:

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