Question

String and Kite were partners, sharing profits and losses in a ratio of 5 : 3. They admitted Spinner as a new partner. String sacrificed 1/4 of his share, and Kite sacrificed 1/6 of his share. What will be the new ratio?

विकल्प

• 6 : 5 : 5

• 9 : 5 : 10

• 15 : 10 : 7

• 35 : 21 : 40

Answer 1

6 : 5 : 5

Explanation:

String’s Sacrifice = `1/4`

Kite’s sacrifice = `1/6` of her original `3/8` share:

Kite’s sacrifice = `1/6 xx 3/8`

= `3/48`

= `1/16`

Calculate New Shares:

String’s New Share = `5/8 - 1/4`

= `(5 xx 4)/(8 xx 4) - (1 xx 8)/(4 xx 8)`

= `20/32 - 8/32`

= `12/32`

= `3/8`

Kite’s New Share = `3/8 - 1/16`

= `(3 xx 2)/(8 xx 2) - 1/16`

= `6/16 - 1/16`

= `5/16`

Spinner’s share is the sum of the sacrificed shares:

Spinner’s Share = `1/4 + 1/16`

= `(1 xx 4)/(4 xx 4) + 1/16`

= `4/16 + 1/16`

= `5/16`

To simplify, use a common denominator of 16:

String’s New Share = `3/8`

= `(3 xx 2)/(8 xx 2)`

= `6/16`

Kite’s New Share = `5/16`

Spinner’s New Share = `5/16`

The new ratio of String, Kite, and Spinner = `6/16 : 5/16 : 5/16` or 6 : 5 : 5