Question

Huma, Hubna and Seema received a total of Rs. 2,016 as monthly allowance from their mother such that Seema gets `1/2` of what Huma gets and Hubna gets `1 2/3` times Seema’s share. How much money do the three sisters get individually?

Answer 1

Seema gets allowance = `1/2` of Huma’s share

Hubna gets allowance = `1 2/3` of Seema’s share

= `5/3` of Seema’s share

= `5/3` of `1/2` of Huma’s share  ...[∵ Seema’s share = `1/2` of Huma’s share]

= `5/3 xx 1/2` of Huma’s share

= `5/6` of Huma’s share

But Huma, Hubna and Seema received total monthly allowance from their mother = ₹ 2016

∴ Huma’s share + Hubna’s share + Seema’s share = ₹ 2016

1 of Huma’s share + `5/6` of Huma’s share + `1/2` of Huma’s share = ₹ 2016

So, `(1 + 5/6 + 1/2)` of Huma’s share = ₹ 2016

⇒ `((6 + 5 + 3)/6)` of Huma’s share = ₹ 2016

⇒ `14/6` of Huma’s share = ₹ 2016

∴ Huma’s share = ₹ `2016 ÷ 14/6`

= ₹ `2016 xx 6/14`

= 144 × 6

= ₹ 864

So, Seema’s share = `1/2` of 864

= `1/2 xx 864`

= ₹ 432

And share = `5/6` of 864

= 5 × 144

= ₹ 720

Hence, Huma, Hubna and Seema get ₹ 864, ₹ 432 and ₹ 720, respectively.