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Question

Mr Raj gave 2/9 of his salary to his wife and paid $1040 for the household bills. After he gave 3/4 of the remaining salary to five of his children to share equally, he had 1/7 of his salary left.

a) Find Mr Raj’s salary

b) Find the amount he had left.

Answer

(a) $5040

(b) $720

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wife :  2/9 of Sal x 7 —>  14/63 of Sal (x7 to change denominator to 63, common multiple of 9 &7)

Household bill : $1040

left: 1/4 of remainder = 1/7 of sal (x 9 to change denominator to 63)

                                         = 9/63 of sal

5 children: 3/4 of remainder = 3/7 of sal (x9 to change denominator to 63)

                                                      = 27/63 of sal

Household bill = 63u-14u-9u-27u

                            = 13u

13u = 1040

1u = 80

a) Mr Raj’s sal = 63u

                           = 63 x 80    

                           = 5040

b) Amt left = 9u

                     = 9 x 80

                     = 720

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thinking if any other method also applicable without using common multiple ( to get 63 ) ? like part and whole ..

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Hi, 

Regardless of the approaches via branching, part-whole or ratio, there is still a need to involve the use of common multiple because salary was indicated as 9 units initially  (2/9 of salary to his wife) and latter as 7units (1/7 of his salary left). 

By Ratio Method:

    W  :  S       5C : R  :  L

     2  :  9         3  :  4 :  1 (1/7 of salary)

     |      |        |      |     |

    14 :  63      27 : 36 : 9

     (× 7)             (×9)

 

   W  : 5C  :  Left  :  HB

   14  :  27  : 9      :    ?

  HB -> 63u – 14u – 27u – 9u

         = 13u

13u = 1040

1u = 80

 

The rest of the steps will follow as per the earlier solution.

 

Hope it clarifies your doubt.

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(a)
9 x 7 = 63
(1/7) x 63 units = 9 units (1/7 of his salary = 1/4 of the remaining salary)
9 units x 4 = 36 units (remaining salary)
(2/9) x 63 units = 14 units (wife)
63 – 14 – 36 = 13
13 units = 1040
63 units = (1040 x 63)/13 = 5040

(b)
5040 x (1/7) = 720

Ans : (a) $5040; (b) $720.

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