Mayank, Mirza, Little and Jaspal bought a motorbike for ₹ 60000. Mayank paid one-half of the sum of the amounts paid by the other boys, Mirza paid one-third of the sum of the amounts paid by the other boys and Little paid one-fourth of the sum of the amounts paid by the other boys. How much did Jaspal have to pay?

### Concept & Strategy The problem tests proportional division of a total sum. The key algebraic insight is that if a person pays a fraction of what the *others* paid, you can easily find their share of the *total* amount. If a person pays $\frac{1}{x}$ of the others, they pay $\frac{1}{x+1}$ of the total sum. ### Step-by-Step Solution * **Given:** Total cost of the motorbike $T = 60000$. * **Calculate Mayank's share:** Mayank pays $\frac{1}{2}$ of the others. Let Mayank's share be $M$. The others paid $(T - M)$. $M = \frac{1}{2}(T - M) \Rightarrow 3M = T \Rightarrow M = \frac{60000}{3} = 20000$. * **Calculate Mirza's share:** Mirza pays $\frac{1}{3}$ of the others. $Mi = \frac{1}{4}T = \frac{60000}{4} = 15000$. * **Calculate Little's share:** Little pays $\frac{1}{4}$ of the others. $L = \frac{1}{5}T = \frac{60000}{5} = 12000$. * **Calculate Jaspal's share:** Jaspal pays the remaining balance. $J = T - (M + Mi + L) = 60000 - (20000 + 15000 + 12000) = 60000 - 47000 = 13000$. ### Exam Strategy & Shortcut Use the ratio-to-fraction shortcut directly: "1/2 of others" $\rightarrow \frac{1}{1+2} = \frac{1}{3}$ of Total. "1/3 of others" $\rightarrow \frac{1}{1+3} = \frac{1}{4}$ of Total. "1/4 of others" $\rightarrow \frac{1}{1+4} = \frac{1}{5}$ of Total. Total fraction paid by the first three = $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{20 + 15 + 12}{60} = \frac{47}{60}$. Jaspal's fraction = $1 - \frac{47}{60} = \frac{13}{60}$. Jaspal's amount = $\frac{13}{60} \times 60000 = 13000$. ### Common Pitfall A very common mistake is calculating the fractions based on the total amount directly (e.g., Mayank = 60000/2 = 30000). The prompt explicitly says "sum of the amounts paid by the *other* boys", not the total amount. ### Final Answer **Therefore, the correct answer is ₹ 13000.**