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Difficulty:
85%
(hard)
Question Stats:
60% (03:05) correct
40%
(03:29)
wrong
based on 25
sessions
History
Date
Time
Result
Not Attempted Yet
Ten years ago, Ulanda allocated 5% of its budget to defense, while its ally Toristan allocated 1%. Since then, Ulanda’s total budget has increased by 20%, and Toristan’s has doubled. Each country now allocates 4% of its current budget to defense.
If the total defense spending of the two countries combined is now 20% greater than it was ten years ago, what is the ratio of Ulanda’s current budget to Toristan’s current budget?
(A) 9 : 4
(B) 12 : 5
(C) 5 : 2
(D) 17 : 5
(E) 17 : 3
If the total defense spending of the two countries combined is now 20% greater than it was ten years ago, what is the ratio of Ulanda’s current budget to Toristan’s current budget?
(A) 9 : 4
(B) 12 : 5
(C) 5 : 2
(D) 17 : 5
(E) 17 : 3
14 Apr 2026, 11:28
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This is a Fractions and Ratios word problem — looks intimidating with all the percentages flying around, but it cleans up fast once you set variables.
Let U = Urlanda's old budget, T = Toristan's old budget.
1. Old defense: Urlanda = 0.05U, Toristan = 0.01T. Combined = 0.05U + 0.01T.
2. New budgets: Urlanda = 1.2U, Toristan = 2T.
3. New defense (each country now spends 4%): Urlanda = 0.04 x 1.2U = 0.048U. Toristan = 0.04 x 2T = 0.08T. Combined new = 0.048U + 0.08T.
4. New combined is 20% more than old combined: 0.048U + 0.08T = 1.2 x (0.05U + 0.01T) = 0.06U + 0.012T.
5. Solve: 0.08T - 0.012T = 0.06U - 0.048U → 0.068T = 0.012U → U/T = 68/12 = 17/3.
6. Current ratio = 1.2U : 2T. Plug in U = (17/3)T: ratio = 1.2 x (17/3) : 2 = 6.8 : 2 = 17 : 5.
Answer: D (17:5).
The classic trap here is forgetting to apply the new budget multipliers at the end (step 6). A lot of people find U/T = 17/3 and then just pick E (17:3) thinking that's the current ratio. But the question asks for the ratio of their CURRENT budgets, which are 1.2U and 2T, not U and T. The 20% growth and doubling change the ratio.
Let U = Urlanda's old budget, T = Toristan's old budget.
1. Old defense: Urlanda = 0.05U, Toristan = 0.01T. Combined = 0.05U + 0.01T.
2. New budgets: Urlanda = 1.2U, Toristan = 2T.
3. New defense (each country now spends 4%): Urlanda = 0.04 x 1.2U = 0.048U. Toristan = 0.04 x 2T = 0.08T. Combined new = 0.048U + 0.08T.
4. New combined is 20% more than old combined: 0.048U + 0.08T = 1.2 x (0.05U + 0.01T) = 0.06U + 0.012T.
5. Solve: 0.08T - 0.012T = 0.06U - 0.048U → 0.068T = 0.012U → U/T = 68/12 = 17/3.
6. Current ratio = 1.2U : 2T. Plug in U = (17/3)T: ratio = 1.2 x (17/3) : 2 = 6.8 : 2 = 17 : 5.
Answer: D (17:5).
The classic trap here is forgetting to apply the new budget multipliers at the end (step 6). A lot of people find U/T = 17/3 and then just pick E (17:3) thinking that's the current ratio. But the question asks for the ratio of their CURRENT budgets, which are 1.2U and 2T, not U and T. The 20% growth and doubling change the ratio.
