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3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times more. What is the ratio of milk to water at the end ?
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In an election between two candidates, y% of the voters did not vote. 10% of the votes cast were declared invalid, while all the valid votes were cast in favour of either of the two candidates. The candidate who got 59.375% of the valid votes cast was declared elected by 2484 votes. If the number of people eligible to vote in that election was 16,000, what is the value of y?
The correct answer is Option 3 i.e. 8.
Let's assume the total polled votes = 100
Total valid votes = 100 × (90/100) = 90
Total no. of votes got by winner = 59.375% of 90 = 53.4375
Other candidates got votes = (90 - 53.4375) = 36.5625
According to the question,
53.4375 - 36.5625 = 2484
⇒ 16.875 = 2484
⇒ 1 = 147.2
So, the total polled votes = 147.2 × 100 = 14720
y% of the voters did not vote
⇒ 16000 × (100 - y)/100 = 14720
⇒ 100 - y = 1472/16
⇒ 100 - y = 92
y = 8
The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?
A 22.5 m high tent is in the shape of a frustum of a cone surmounted by a hemisphere. If the diameters of the upper and the lower circular ends of the frustum are 21 m and 39 m respectively, then find the area of cloth (in m2) used to make the tent (ignoring the wastage).
A tangent at point A of a circle of radius 6 cm meets a line through the centre O at point B. If OB = 10 cm, then the length of AB (in cm) is equal to:
The correct answer is option 4 i.e. 8.
Given that
A circle of radius (r) = 6 cm
OB = 10 cm
A line PQ through the center O meets at point B
PQ = 2 × 6 = 12 cm,
PB = OP + OB = 6 + 10 = 16 cm,
QB = OB - OQ = 10 - 6 = 4 cm
According to the tangent theorem
AB2 = PB × QB
⇒ AB2 = 16 × 4 = 64
⇒ AB = 8 cm
The compound interest and the amount obtained on a certain sum of money are ₹820 and ₹8,820, respectively, after 2 years. If the rate of interest is compounded yearly, then the rate of interest is:
The following table shows the number of sweets manufactured by six factories.
What is the respective ratio of sweets manufactured by factories P, Q and R together in the year 2023, to the sweets manufactured by factories S, T and U together in the same year?
The correct answer is option 1 i.e. 568 : 499.
The sweets manufactured by factories P. Q and R together in the year 2023 = 178 + 240 + 150 = 568
The sweets manufactured by factories S.T and U together in the same year 2023 = 130 + 177 + 192 = 499
Hence, the required ratio is 568 : 499
A pipe can fill a tank in 30 minutes. Due to two leakages A and B, the filled tank would be drained off in hour, respectively. How long will it take to fill the tank if the pipes A and B are left open?
The curved surface area of a solid cylinder of height 15 cm is 660 cm2. What is the volume (in cm3) of the cylinder?
The correct answer is option 3 i.e. 2310.
The curved surface area of a solid cylinder of height 15 cm is 660 cm2
CSA of cylinder = 2πrh
The volume of the cylinder = π r2 h
⇒ CSA = 2 × (22/7) × r × 15
⇒ 660 = 660/7 × r
⇒ r = 7 cm
Volume of cylinder = (22/7) × 49 × 15 = 2310 cm3
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