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Quantitative Aptitude [ Question No: 1 To 20 ] :
Direction for [ Question No: 1 To 1 ] :
The stacked bar chart below shows the production of three different crops (Wheat, Rice, and Maize) in a state over six years (in lakh tonnes). Study the chart to answer the questions.
The production of Wheat in 2016 is what percentage of the production of Rice in 2020?
A container of milk was \(\frac{3}{4}\) full. When 5 bottles of milk were taken out and 3 bottles of milk were poured into it, it was \(\frac{2}{3}\) full. How many bottles of milk can the container contain ?
PQRS is a parallelogram whose diagonals PR and QS intersect at a point O such that OP = \((x + 7)\) cm, OQ = \((x + y)\) cm, OR = 20 cm and OS = 16 cm. Then, value of \((7y + 5)\) (in cm) is :
In a pentagon ABCDE, \(\angle A = (2x + 9^\circ)\), \(\angle B = (2x + 1^\circ)\), \(\angle C = (2x - 1^\circ)\), \(\angle D = (2x + 5^\circ)\) and \(\angle E = (2x - 4^\circ)\). Then, value of \((2x + 10^\circ)\) is :
R needs ₹1,50,000 as income from his investments. He deposited ₹8,00,000 in a bank which gives ₹4,500 as interest per lakh. He deposited ₹6,00,000 in the post office which gives ₹50,000 as interest and the rest in the share market. In the share market, he earns ₹1,500 for every ₹25,000. How much money did he invest in the share market?
One of the factors of \(81x^{2} - 126xy + 49y^{2} - (5x + 3y)^{2}\) is
When a polynomial \(P(x) = x^3 + 2x^2 - 5x + 7\) is divided by \((x-2)\), what is the remainder?
What is the value of \(\sqrt{6+\sqrt{6+\sqrt{6+...}}}\) ?
At a certain moment the length of the shadow of a pole is \( \sqrt{3} \) times the height of the pole. The angle of elevation of the sun is:
A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° respectively. What is the height of the tower?
The banker’s discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is
An accurate clock is started at noon. By 10 minutes past 3, the hour hand has turned through:
The area of a field in the shape of a trapezium measures 1440 m². The perpendicular distance between the parallel side is 24m. If the ratio of the parallel sides is 5:3, what is the length of the longer parallel side?
A shuttlecock used for playing badminton has the shape of the combination of
Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the stream is 2 km/hr, what is the speed of the boat in still water ?
Ajay takes 4 hours more while swimming upstream than downstream. His speed in still water is 10 km/hr. The speed of stream is 2 km/hr. What is the distance?
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
Quantitative Aptitude [ Question No: 1 To 20 ] :
Direction for [ Question No: 1 To 1 ] :
The stacked bar chart below shows the production of three different crops (Wheat, Rice, and Maize) in a state over six years (in lakh tonnes). Study the chart to answer the questions.
The production of Wheat in 2016 is what percentage of the production of Rice in 2020?
Your Answer : (Not Answered)
Correct Answer : C
Production of Wheat in 2016 = 40 lakh tonnes.
Production of Rice in 2020 = 50 lakh tonnes.
Required Percentage = \(\frac{\text{Wheat 2016}}{\text{Rice 2020}} \times 100\)
= \(\frac{40}{50} \times 100 = 80\)%.
A container of milk was \(\frac{3}{4}\) full. When 5 bottles of milk were taken out and 3 bottles of milk were poured into it, it was \(\frac{2}{3}\) full. How many bottles of milk can the container contain ?
Your Answer : (Not Answered)
Correct Answer : B
The container holds 24 bottles of milk.
Let the capacity be C bottles. Taking out 5 bottles and pouring in 3 is a net loss of 2 bottles, which takes the level from three-quarters to two-thirds:
\[ \begin{aligned} \tfrac{3}{4}C - 2 &= \tfrac{2}{3}C \\ \tfrac{1}{12}C &= 2 \\ C &= 24 \end{aligned} \]
Check: three-quarters of 24 is 18; after losing 2 bottles it holds 16, which is two-thirds of 24.
12 comes from treating the net change as 1 bottle, and 20 and 15 give non-whole quarter or third fills, so they cannot fit.
PQRS is a parallelogram whose diagonals PR and QS intersect at a point O such that OP = \((x + 7)\) cm, OQ = \((x + y)\) cm, OR = 20 cm and OS = 16 cm. Then, value of \((7y + 5)\) (in cm) is :
Your Answer : (Not Answered)
Correct Answer : C
The value of \(7y + 5\) is 26.
The diagonals of a parallelogram bisect each other, so OP = OR and OQ = OS:
\[ \begin{aligned} x + 7 &= 20 \Rightarrow x = 13 \\ x + y &= 16 \Rightarrow y = 3 \\ 7y + 5 &= 21 + 5 = 26 \end{aligned} \]
21 is 7y without the 5. Equating OP with OQ instead of with OR, as if all half-diagonals were equal, is the usual slip behind the other values.
In a pentagon ABCDE, \(\angle A = (2x + 9^\circ)\), \(\angle B = (2x + 1^\circ)\), \(\angle C = (2x - 1^\circ)\), \(\angle D = (2x + 5^\circ)\) and \(\angle E = (2x - 4^\circ)\). Then, value of \((2x + 10^\circ)\) is :
Your Answer : (Not Answered)
Correct Answer : C
The value of \((2x + 10^\circ)\) is 116°.
The interior angles of a pentagon add up to \((5 - 2) \times 180^\circ = 540^\circ\).
\[ \begin{aligned} 10x + (9 + 1 - 1 + 5 - 4)^\circ &= 540^\circ \\ 10x + 10^\circ &= 540^\circ \\ x &= 53^\circ \end{aligned} \]
So \(2x + 10^\circ = 106^\circ + 10^\circ = 116^\circ\). The other three values would each need a different x, and none of those makes the five angles add up to 540°.
R needs ₹1,50,000 as income from his investments. He deposited ₹8,00,000 in a bank which gives ₹4,500 as interest per lakh. He deposited ₹6,00,000 in the post office which gives ₹50,000 as interest and the rest in the share market. In the share market, he earns ₹1,500 for every ₹25,000. How much money did he invest in the share market?
Your Answer : (Not Answered)
Correct Answer : C
R invested between Rs 10,00,000 and Rs 11,00,000 in the share market, about Rs 10.67 lakh. The bank pays Rs 4,500 per lakh, so on Rs 8 lakh it pays
\[ 8 \times 4500 = 36000 \]The post office pays Rs 50,000. The required income of Rs 1,50,000 leaves
\[ 150000 - 36000 - 50000 = 64000 \]from the share market. It pays Rs 1,500 on Rs 25,000, which is 6 percent, so the amount invested is
\[ \frac{64000}{0.06} \approx 1066667 \]This lies in the 10 to 11 lakh range and not in the other three ranges.
One of the factors of \(81x^{2} - 126xy + 49y^{2} - (5x + 3y)^{2}\) is
Your Answer : (Not Answered)
Correct Answer : C
One factor is 7x - 2y.
The first three terms form a perfect square, so the expression is a difference of two squares:
\[ \begin{aligned} &(9x - 7y)^{2} - (5x + 3y)^{2} \\ &= (9x - 7y - 5x - 3y)(9x - 7y + 5x + 3y) \\ &= (4x - 10y)(14x - 4y) \\ &= 4(2x - 5y)(7x - 2y) \end{aligned} \]
So the factors are 2x - 5y and 7x - 2y. Options A and B have the right numbers with the wrong sign (7x + 2y, 2x + 5y), and 5x - 7y does not appear at all.
When a polynomial \(P(x) = x^3 + 2x^2 - 5x + 7\) is divided by \((x-2)\), what is the remainder?
Your Answer : (Not Answered)
Correct Answer : C
According to the Polynomial Remainder Theorem, if a polynomial P(x) is divided by \((x-a)\), the remainder is P(a). Here, the divisor is \((x-2)\), so a=2. We need to calculate P(2). \(P(2) = (2)^3 + 2(2)^2 - 5(2) + 7 = 8 + 2(4) - 10 + 7 = 8 + 8 - 10 + 7 = 16 - 10 + 7 = 6 + 7 = 13\). The remainder is 13.
What is the value of \(\sqrt{6+\sqrt{6+\sqrt{6+...}}}\) ?
Your Answer : (Not Answered)
Correct Answer : B
Let \(x = \sqrt{6+\sqrt{6+\sqrt{6+...}}}\).
Then, we can write \(x = \sqrt{6+x}\).
Squaring both sides, we get \(x^2 = 6+x\).
\(x^2 - x - 6 = 0\).
Factoring the quadratic equation: \((x-3)(x+2) = 0\).
Since the value inside the square root is positive, x must be positive. So, x = 3.
At a certain moment the length of the shadow of a pole is \( \sqrt{3} \) times the height of the pole. The angle of elevation of the sun is:
Your Answer : (Not Answered)
Correct Answer : A
The angle of elevation \( \theta \) satisfies
\[ \tan\theta = \frac{\text{height of pole}}{\text{length of shadow}} \]
With the shadow \( \sqrt{3} \) times the height \( h \):
\[ \tan\theta = \frac{h}{\sqrt{3}\,h} = \frac{1}{\sqrt{3}} \quad\Longrightarrow\quad \theta = 30^{\circ} \]
The pole's height cancels, so no measurement is needed. A shadow longer than the object always means the sun is below \( 45^{\circ} \).
A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° respectively. What is the height of the tower?
Your Answer : (Not Answered)
Correct Answer : C
Let the tower be \( h \) m and the observer \( d \) m away. The bottom of the flagpole is the top of the tower.
\[ \tan 30^{\circ} = \frac{h}{d} \quad\Longrightarrow\quad d = h\sqrt{3} \]
\[ \tan 60^{\circ} = \frac{h + 18}{d} \quad\Longrightarrow\quad h + 18 = \sqrt{3}\,d = \sqrt{3}\cdot h\sqrt{3} = 3h \]
\[ 2h = 18 \quad\Longrightarrow\quad h = 9 \text{ m} \]
Because \( \tan 60^{\circ} / \tan 30^{\circ} = 3 \), the full height is exactly three times the tower - so the flagpole is twice the tower, and 18 m makes the tower 9 m.
The banker’s discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is
Your Answer : (Not Answered)
Correct Answer : B
S.I. on Rs. 1600 = T.D. on Rs. 1680.
=> Rs. 1600 is the P.W. of Rs. 1680,
=> Rs. 80 is S.I. on Rs. 1600 at 15%.
=> 80 = 1600*T*15/100
=> 80 = 16*T*15
=> 5 = T*15
=> T = 1/3 year = 12/3 months
= 4 months
An accurate clock is started at noon. By 10 minutes past 3, the hour hand has turned through:
Your Answer : (Not Answered)
Correct Answer : B
The hour hand turns \( 30^{\circ} \) an hour, or \( 0.5^{\circ} \) a minute.
From noon to 3:10 is \( 3\tfrac{1}{6} \) hours:
\[ 3\tfrac{1}{6} \times 30 = 95^{\circ} \]
The extra ten minutes contribute \( 10 \times 0.5 = 5^{\circ} \), which is what lifts the answer above the whole-hour figure.
The area of a field in the shape of a trapezium measures 1440 m². The perpendicular distance between the parallel side is 24m. If the ratio of the parallel sides is 5:3, what is the length of the longer parallel side?
Your Answer : (Not Answered)
Correct Answer : A
Given, ratio of the parallel sides of a trapezium = 5 : 3
---> Let the parallel sides (ie., 'a' and 'b') be 5x and 3x respectively.
Given, perpendicular distance = height = 24 m
and Area = 1440 m2
Formula: Area of Trapezium = (1/2) * h * (a + b)
---> 1440 = (1/2) * 24 * (5x + 3x)
---> 1440 = 12 * (8x)
---> 120 = 8x
---> 15 = x
Thus, parallel sides, a = 5x = 5 * 15 = 75 m
and b = 3x = 3 * 15 = 45 m
Hence, Longer parallel side is 'a' = 75 m
Smaller parallel side is 'b' = 45 m.
A shuttlecock used for playing badminton has the shape of the combination of
Your Answer : (Not Answered)
Correct Answer : D
A shuttlecock has a rounded cork base and a skirt of feathers that flares outward from it.
The cork nose is a hemisphere. The feather skirt is narrow where it meets the cork and wide at the open end, with both ends circular and neither closing to a point - that is a frustum of a cone.
A full cone would come to a point at the top, and a cylinder would keep the same width all the way up; neither matches the flare.
Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Your Answer : (Not Answered)
Correct Answer : B
"6 paisa per month" means 6 paise on each rupee each month, or 6% per month.
\[ \text{SI} = 500 \times \frac{6}{100} \times 9 \]
\[ = 500 \times 0.06 \times 9 = \text{Rs. } 270 \]
The rate is already monthly, so the nine months are used directly - no conversion to years is needed.
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Your Answer : (Not Answered)
Correct Answer : C
Take the quantities as 1, 1 and 2 kg, four kilograms in all.
\[ 126 + 135 + 2p = 4 \times 153 = 612 \]
\[ 2p = 612 - 261 = 351 \quad\Longrightarrow\quad p = \text{Rs. } 175.50 \]
The third variety carries half the weight of the mixture, which is why its price does not have to be far above 153 to lift the average.
A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the stream is 2 km/hr, what is the speed of the boat in still water ?
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: 10 km/hr
With \(b\) the still-water speed, the two times differ by \(1\tfrac{1}{2}\) hours:
\[\frac{36}{b-2} - \frac{36}{b+2} = 1.5\]
\[36 \cdot \frac{(b+2)-(b-2)}{b^2 - 4} = 1.5 \quad\Longrightarrow\quad \frac{144}{b^2 - 4} = 1.5\]
\[b^2 - 4 = 96 \quad\Longrightarrow\quad b^2 = 100 \quad\Longrightarrow\quad b = 10 \text{ km/hr}\]
Checking: 36 km takes 3 hours downstream at 12 km/hr and 4.5 hours upstream at 8 km/hr.
Ajay takes 4 hours more while swimming upstream than downstream. His speed in still water is 10 km/hr. The speed of stream is 2 km/hr. What is the distance?
Your Answer : (Not Answered)
Correct Answer : A
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 12 \text{ km/h}, \qquad b - r = 8 \text{ km/h} \]
The upstream trip takes 4 hours longer over the same distance \( D \):
\[ \frac{D}{8} - \frac{D}{12} = 4 \]
\[ D\left(\frac{3 - 2}{24}\right) = 4 \quad\Longrightarrow\quad \frac{D}{24} = 4 \]
\[ D = 96 \text{ km} \]
Checking: 12 hours upstream against 8 hours downstream - a difference of exactly 4.
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
Your Answer : (Not Answered)
Correct Answer : C
| Work done by the waste pipe in 1 minute = | 1 | - |  |
1 | + | 1 |  |
| 15 | 20 | 24 |
| = | |
1 | - | 11 | |
| 15 | 120 |
| = - | 1 | . [-ve sign means emptying] |
| 40 |
 Volume of |
1 | part = 3 gallons. |
| 40 |
Volume of whole = (3 x 40) gallons = 120 gallons.
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Your Answer : (Not Answered)
Correct Answer : D
Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).
\[ \frac{1}{10} + \frac{1}{15} - \frac{1}{w} = \frac{1}{18} \]
\[ \frac{3 + 2}{30} - \frac{1}{w} = \frac{1}{18} \quad\Longrightarrow\quad \frac{1}{6} - \frac{1}{w} = \frac{1}{18} \]
\[ \frac{1}{w} = \frac{3 - 1}{18} = \frac{1}{9} \quad\Longrightarrow\quad w = 9 \text{ minutes} \]
Marks
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20