Question

A sum of r is divided between A,B,C and D such that the ratio of shares of A and B is 9:5, C's share
is 70% of B's share and the ratio of the share of D to the combined share of B and C is 1:3. If the share
of A is INR 999, the value of x is​

Answer 1

Answer:

Let the shares of A,B,C,D, be Rs3x,Rs5x,Rs7xandRs11x respectively.

Then, 7x−3x=1668⇒4x=1668⇒x=417∴B

′

share+D

′

share=5x+11x=Rs16x=16×417=Rs6672

Answer 2

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

$\huge\bf\underline{\underline{\red{GIVEN :}}}$

$\red\bigstar$ The Ratio of shares of A & B is 9:5.

$\red\bigstar$ Share of C is 70% of B's share.

$\red\bigstar$ The Ratio of the share of D to the combined share of B & C is 1:3.

$\red\bigstar$ The share of A is INR 999.

$\huge\bf\underline{\underline{\red{TO \: FIND :}}}$

$\red\bigstar$ The value of x.

$\huge\bf\underline{\underline{\red{SOLUTION :}}}$

$\red\bigstar$ Let A = 9k & B = 5k.

We know that C's share is 70% of B's share,

$➞ \: C's \: share \: = \frac{70}{100} \times 5k$

$➞ \: C's \: share = 3.5k$

We also know that the share of D to the combined share of B & C is 1:3,

$➞ \: \frac{D }{(5k + 3.5k)} = \frac{1}{3}$

$➞ \: D = \frac{(5k + 3.5k)}{3}$

$➞ \: D = \frac{8.5k}{3}$

⠀

⠀⠀⠀⠀⠀⠀$\red\bigstar \: A = 9k$

⠀⠀⠀⠀⠀⠀$\red\bigstar \: B = 5k$

⠀⠀⠀⠀⠀⠀$\red\bigstar \: C = 3.5k$

⠀⠀⠀⠀⠀⠀$\red\bigstar \: D = \frac{8.5k}{3}$

The share of A is 999 INR,

$9k = 999$

$➞ \: k = \frac{999}{9}$

$➞ \: k = 111$

Now put the values,

⠀⠀$A = 9k$

$➞ \: A = 9 \times 111$

$➞ \: A = 999$

⠀

⠀⠀$B = 5k$

$➞ \: B = 5 \times 111$

$➞ \: B = 555$

⠀

⠀⠀$C = 3.5k$

$➞ \: C = 3.5 \times 111$

$➞ \: C = 388.5$

⠀

⠀⠀$D = \frac{8.5k}{3}$

$➞ \: D = \frac{8.5k}{3} \times 111$

$➞ \: D = 314.5$

⠀

The value of x,

$x = 999 + 555 + 388.5 + 314.5$

$x = \small\boxed{{\sf\red{ \: 2257 \: }}}$

⠀

$\huge\boxed{{\sf\red{Hence, \: the \: value \: of \: x \: is \: 2257.}}}$

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