The ratio of the areas of two similar triangles is 49:64. Find the ratio of their corresponding sides.
Correct answer: 7:8
Explanation: Side ratio is square root of area ratio =7:8.
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If the roots of x²−15x+54=0 are α and β, find α−β.
Correct answer: 3
Explanation: Roots are 6 and 9, difference=3.
A train running at 90 km/h crosses a bridge in 32 seconds and a pole in 20 seconds. Find the length of the bridge.
Correct answer: 300 m
Explanation: Speed=25 m/s. Train length=500 m. Bridge length=800−500=300 m.
The average of 25 numbers is 64. If one observation 82 is replaced by 57, find the new average.
Correct answer: 63
Explanation: Total decreases by25, average decreases by1.
A and B together complete a work in 12 days. A alone takes 20 days. In how many days can B alone complete the work?
Correct answer: 28
Explanation: B's efficiency =1/12−1/20=1/30. Hence B takes 30 days.
A trader marks an article 50% above cost price and allows a discount of 12%. Find the profit percentage.
Correct answer: 32%
Explanation: Assume CP=100. MP=150. SP=150×0.88=132. Profit=32%.
The HCF of two numbers is 18 and their product is 58320. If their LCM is 180, find the larger number.
Correct answer: 324
Explanation: Let numbers be 18a and 18b where HCF(a,b)=1. Product=HCF×LCM=3240? Using Product=58320 gives second number after factorization =324.
The product of two consecutive integers is 306. Find the larger integer.
Correct answer: 18
Explanation: 17×18=306.
Find the compound interest on ₹20000 at 5% per annum for 2 years.
Correct answer: ₹2025
Explanation: CI=20000×(1.05²−1)=2025.
A boat travels 54 km downstream in 3 hours and 30 km upstream in 3 hours. Find the speed of the stream.
Correct answer: 4 km/h
Explanation: Downstream=18, upstream=10, stream=(18−10)/2=4.
The ratio of radii of two circles is 4:7. Find the ratio of their areas.
Correct answer: 16:49
Explanation: Area ∝ radius².
If x²−9x+20=0, find the larger root.
Correct answer: 5
Explanation: Factors are (x−4)(x−5)=0.
A train 180 m long crosses a pole in 9 seconds. Find its speed.
Correct answer: 72 km/h
Explanation: Speed =180/9=20 m/s =72 km/h.
The average of 20 numbers is 36. If one number 48 is replaced by 68, find the new average.
Correct answer: 37
Explanation: Increase in total =20, average increases by 1.
A can finish a work in 15 days and B in 20 days. They work together for 5 days. What fraction of work remains?
Correct answer: 5/12
Explanation: Completed work = 5×(1/15+1/20)=7/12, remaining = 5/12.
A number is increased by 25% and then decreased by 20%. What is the net percentage change?
Correct answer: No change
Explanation: 125×80/100 = 100, therefore there is no net change.
If the HCF of two numbers is 16 and their LCM is 960, one number being 160, find the other number.
Correct answer: 96
Explanation: Using Product = HCF × LCM, second number = (16×960)/160 = 96.
The ratio of the radii of two circles is 3:5. Find the ratio of their areas.
Correct answer: 9:25
Explanation: Area is proportional to square of radius. Hence ratio=9:25.
The smallest number which when divided by 18, 24 and 30 leaves remainder 5 in each case is
Correct answer: 365
Explanation: Required number = LCM(18,24,30)+5 = 360+5 =365.
Find the compound interest on ₹13000 at 10% per annum for 2 years.
Correct answer: ₹2860
Explanation: CI=13000×(1.1²−1)=2730.