Discussion
Mala and Latha each had a number of bangles. Mala said to Latha "If you give me 4 of your bangles, my number will be thrice yours". Latha replied "If you give me 36, my number will be thrice yours". What is the total bangles together with them?
Answer: B
Together they have 80 bangles.
Let Mala have \(m\) and Latha \(l\) bangles.
\[ \begin{aligned} m + 4 &= 3(l - 4) \Rightarrow m = 3l - 16 \\ l + 36 &= 3(m - 36) \\ l + 36 &= 9l - 48 - 108 \Rightarrow l = 24 \end{aligned} \]
Then \(m = 56\), and the total is 80. Check: if Latha gives 4, Mala has 60 and Latha 20; if Mala gives 36, Latha has 60 and Mala 20. Both times one has three times the other.
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