Subject
Quantitative Aptitude
Topic
Age
x years ago, Apu was one fifth as old as Topu. In x years, Topu will be twice as old as Apu. What is the ratio of Apu's current age to Topu's current age?
x years ago, Apu was one fifth as old as Topu. In x years, Topu will be twice as old as Apu. What is the ratio of Apu's current age to Topu's current age?
ক)
2 : 5খ)
5 : 7গ)
3 : 7ঘ)
5 : 13ঙ)
NoneExplanation
ধরি, Apu'র বর্তমান বয়স = a বছর Topu'র বর্তমান বয়স = t বছর x বছর আগে, Apu'র বয়স = (a - x) বছর Topu'র বয়স = (t - x) বছর সুতরাং, (a - x) = (t - x)/5 [কারণ Apu ছিল Topu'র বয়সের এক-পঞ্চমাংশ] ⇒ 5(a - x) = (t - x) ...(1) x বছর পরে, Apu'র বয়স = (a + x) বছর Topu'র বয়স = (t + x) বছর সুতরাং, (t + x) = 2(a + x) [কারণ Topu হবে Apu'র দ্বিগুণ বয়সী] ⇒ t + x = 2a + 2x ...(2) সমীকরণ (1) থেকে, 5a - 5x = t - x ⇒ t = 5a - 4x ...(3) এটি সমীকরণ (2) তে বসিয়ে, 5a - 4x + x = 2a + 2x ⇒ 5a - 3x = 2a + 2x ⇒ 5a - 2a = 2x + 3x ⇒ 3a = 5x ⇒ x = 3a/5 এই x এর মান সমীকরণ (3) এ বসিয়ে, t = 5a - 4(3a/5) ⇒ t = 5a - 12a/5 ⇒ t = (25a - 12a)/5 ⇒ t = 13a/5 তাহলে a : t = a : 13a/5 = 5 : 13 সুতরাং Apu'র বর্তমান বয়স : Topu'র বর্তমান বয়স = 5 : 13Related questions
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