Delhi Police Constable practice question
Two positive integers x and y are such that log₁₀x + log₁₀y = 4, and x : y = 25 : 4. Find the value of x + y.
From a Delhi Police Constable Quantitative Aptitude practice set · Quantitative Aptitude
Tap an option to check your answer.
Show answer and explanation
Correct answer: (A) 290
log₁₀x + log₁₀y = 4 gives, by the product rule, log₁₀(xy) = 4, so xy = 10⁴ = 10000. Since x:y = 25:4, let x = 25k and y = 4k. Then xy = 100k² = 10000, so k² = 100, k = 10. Thus x = 250, y = 40, and x + y = 290.
हिंदी में प्रश्न
दो धनात्मक पूर्णांक x और y इस प्रकार हैं कि log₁₀x + log₁₀y = 4 है, तथा x : y = 25 : 4 है। x + y का मान ज्ञात कीजिए।
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
उत्तर और व्याख्या देखें
सही उत्तर: (A) 290
log₁₀x + log₁₀y = 4 से, गुणनफल नियम द्वारा, log₁₀(xy) = 4, अतः xy = 10⁴ = 10000. चूँकि x:y = 25:4 है, मान लीजिए x = 25k और y = 4k. तब xy = 100k² = 10000, अतः k² = 100, k = 10. इस प्रकार x = 250, y = 40, तथा x + y = 290।
More solved Quantitative Aptitude questions
- In triangle ABC, D and E are points on AB and AC respectively such that DE is parallel to BC, and AD : DB = 1 : 4. If BC = 30 cm, find the…
- Convert a speed of 17 m/s into km/hr.
- If 21 men working 6 hours a day can complete 1 unit(s) of work in 18 days, in how many days can 7 men working 8 hours a day complete 2…
- The average age of 15 persons increases by 2.5 years when a person aged 27 years is replaced by a new person. Find the age of the new…
- A trade bill worth Rs. 1200 is due 3 years from now. If the prevailing interest rate is 8% per annum, find the present worth of the sum…
- Two towers of equal height stand on opposite sides of a straight road that is 160 m wide. From a point on the road between the two towers…