Huma, Hubna and Seema received a total of ₹ 2,016 as monthly allowan

1.	Huma, Hubna and Seema received a total of ₹ 2,016 as monthly allowance from their mother such that Seema gets ½ of what Huma gets and Hubna gets 1 2/3 times Seema’s share. How much money do the three sisters get individually?
Answer» From the question it is given that, Total monthly allowance received by Huma, Hubna and Seem = ₹ 2,016 from their mother Seema gets allowance = ½ of Huma’s share Hubna gets allowance = 1 2/3 of Seema’s share = 5/3 of Seema’s share = 5/3 of ½ of Huma’s share … [∵ given] = 5/3 × ½ of Huma’s share = 5/6 of Huma’s share So, Huma’s share + Hubna’s share + Seema’s share = ₹ 2,016 Let Huma’s share be 1, 1 + (5/6) Huma’s share + ½ Huma’s share = ₹ 2,016 (1 + (5/6) + ½) = ₹ 2,016 The LCM of the denominators 1, 6 and 2 is 6 (1/1) = [(1×6)/ (1×6)] = (6/6) (5/6) = [(5×1)/ (6×1)] = (5/6) (1/2) = [(1×3)/ (2×3)] = (3/6) Then, (6/6) + (5/6) + (3/6) = ₹ 2,016 (6 + 5 + 3)/ 6 = ₹ 2,016 (14/6) = ₹ 2,016 So, Huma’s share = ₹ 2,016 ÷ (14/6) = 2,016 × (6/14) = 144 × 6 ∴Huma’s Share is = ₹ 864 Seema’s share = ½ Huma’s share = ½ × 864 = ₹ 432 Hubna’s share = 5/6 of Huma’s share = 5/6 × 864 = 5 × 144 = ₹ 720

Huma, Hubna and Seema received a total of ₹ 2,016 as monthly allowance from their mother such that Seema gets ½ of what Huma gets and Hubna gets 1 2/3 times Seema’s share. How much money do the three sisters get individually?

Answer»

From the question it is given that,

Total monthly allowance received by Huma, Hubna and Seem = ₹ 2,016

from their mother

Seema gets allowance = ½ of Huma’s share

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

= 5/3 of Seema’s share

= 5/3 of ½ of Huma’s share … [∵ given]

= 5/3 × ½ of Huma’s share

= 5/6 of Huma’s share

So,

Huma’s share + Hubna’s share + Seema’s share = ₹ 2,016

Let Huma’s share be 1,

1 + (5/6) Huma’s share + ½ Huma’s share = ₹ 2,016

(1 + (5/6) + ½) = ₹ 2,016

The LCM of the denominators 1, 6 and 2 is 6

(1/1) = [(1×6)/ (1×6)] = (6/6)

(5/6) = [(5×1)/ (6×1)] = (5/6)

(1/2) = [(1×3)/ (2×3)] = (3/6)

Then,

(6/6) + (5/6) + (3/6) = ₹ 2,016

(6 + 5 + 3)/ 6 = ₹ 2,016

(14/6) = ₹ 2,016

So, Huma’s share = ₹ 2,016 ÷ (14/6)

= 2,016 × (6/14)

= 144 × 6

∴Huma’s Share is = ₹ 864

Seema’s share = ½ Huma’s share

= ½ × 864

= ₹ 432

Hubna’s share = 5/6 of Huma’s share

= 5/6 × 864

= 5 × 144

= ₹ 720