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 times Seema’s share. How much money do the three sisters get individually?
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 = 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