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What are the marks obtained by Rishab (assuming Amay scored more)?
Statement I: The sum of their scores form 70% of the total score.
Statement II: The ratio of the sum of marks of Amay and Rishab to the difference of their marks is 17:3 and the square of three-fourth of four-fifth of half of Amay's marks is 250000.
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The correct answer is Option 2 i.e. Only Statement II is sufficient
We have the ratio of the sum and difference of their marks and what percent the sum of their score makes out of the total marks.
From S1, we have -
R + A = 70% of the total marks
We cannot take out the marks scored by Rishab through this as we do not have the total score.
From S2, we have -
Marks scored by Amay = 250000−−−−−−√250000 × 2 × (4/5) × (3/4) = 500 × 2 × (3/5) = 600
(A + R)/(A - R) = 17/3
⇒ 17A - 17R = 3A + 3R
⇒ 14A = 20R
⇒ A/R = 20/14 = 10/7
⇒ 600/R = 10/7
⇒ R = (600 × 7)/10
R = 420
There are two vessels A and B. Vessel A contains 105 liters of pure milk and vessel B contains 85 liters of pure water. 5L of milk is taken out from vessel A and poured into vessel B. Then, 9 liters of mixture (milk and water) is taken out from vessel B and poured into vessel A. What is the ratio of the quantity of milk in vessel A to the quantity of pure water in vessel B?
The following table shows the number of students in different streams in 5 departments. Study the table carefully and answer the question based on the table.
Which department has the minimum number of students in all streams?
The correct answer is Option 2 i.e. A.
Department A = 400 + 750 + 350 + 250 = 1750 [Minimum]
Department B = 500 + 600 + 400 + 300 = 1800
Department C = 350 + 700 + 450 + 380 = 1880
Department D = 300 + 500 + 500 + 550 = 1850
Department E = 600 + 450 + 750 + 600 = 2400
The average height of a certain number of students in a group is 155.6 cm. If 12 students having an average height of 150.5 cm join the group and 7 students having an average height of 159 cm leave the group, the average height of the students in the group will decrease by 34 mm. What is the number of students, initially, in the group?
If (x + y)3 + 27(x - y)3 = (Ax - 2y)(Bx2 + Cxy + 13y2), then the value of (2A + B + C) is:
The correct answer is option 3 i.e. -1.
(x + y)3 + 27(x - y)3 = (Ax - 2y)(Bx2 + Cxy + 13y2)
⇒ 28x3 - 78x2y + 84xy2 - 26y3 = ABx3 + (AC - 2B)x2y + (13A - 2C)xy2 - 26y3
Compare coefficients: AB = 28
AC - 2B = -78
13A - 2C = 84
Try A = 4, then B = 7 (since 4 × 7 = 28)
Also, 13(4) - 2C = 84 ⇒ C = - 16
2A + B + C = 2(4) + 7 + (-16) = 8 + 7 - 16 = -1
Find the smallest 5-digit number which when divided by 15, 20 and 25 leaves remainders 7, 12 and 17, respectively.
The correct answer is option 3 i.e. 10192.
15 - 7 = 8; 20 - 12 = 8; 25 - 17 = 8
LCM of 15, 20, and 25 = 300
The smallest 5-digit number is 10000
10000 = 300 × 33 + 100
300 - 100 = 200
Required number = 10000 + 200 - 8 = 10192
Therefore, the required number is 10192.
When a trader sells a bull at 25% loss and a camel at 15% profit, he neither gains nor loses in the total trade. When he sells the bull at 10% loss and the camel at 20% profit, what will be his overall profit or loss in the business?
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