Kaprekar Contest (NMTC Sub-Junior 2018 - VII and VIII Grades) - Stage I- Problems and Solution
Join Trial or Access Free ResourcesJoin Trial or Access Free ResourcesThe fraction greater than $8 \frac{4}{9}$ is
(A) $8 \frac{1}{3}$
(B) $\frac{150}{18}$
(C) $8 \frac{2}{3}$
(D) $\frac{216}{27}$
A car is slowly driven in a road full of fog. The car passes a man who was walking at the rate of 3 $\mathrm{km}$ an hour in the same direction. He could see the car for 4 minutes and was visible for up to a distance of 100 meters. The speed of the car is (in $\mathrm{km}$ per hours)
(A) $4 \frac{1}{2}$
(B) $4$
(C) $3 \frac{1}{2}$
(D) $3$
Kiran sells pens at a profit of $20 \%$ for Rs. 60 . But due to lack of demand he reduced its price to Rs. 55. Then
(A) He gets a profit of $10 \%$
(B) He gets a profit of $12 \%$
(C) He incurs a loss of $10 \%$
(D) He incurs a loss of $8 \%$
If $40 \%$ of a number is added to another number then it becomes $125 \%$ of itself. The ratio of the second to the first number is
(A) $5: 8$
(B) $7: 5$
(C) $8: 5$
(D) None of these
The length of a rectangular sheet of paper is $33 \mathrm{~cm}$. It is rolled along its length into a cylinder so that width becomes height of the cylinder. The volume is 1386 cubic cms. The width of the rectangular sheet (in $\mathrm{cm}$ ) is
(A) 14
(B) 15
(C) 16
(D) 18
If $\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\ldots \ldots . .+\frac{1}{\mathrm{n} \times(\mathrm{n}+1)}=\frac{19}{20}$ then $\mathrm{n}=$
(A) 18
(B) 19
(C) 20
(D) 25
$a, b$ are natural numbers. If $9 a^2=12 a+96$ and $b^2=2 b+3$, the value of $2018(a+b)$ is
(A) 14226
(B) 14128
(C) 14126
(D) 14246
Shanti has three daughters. The average age of them is 15 years. Their ages are in the ratio $3: 5$ : 7. The age of the youngest daughter is (in years)
(A) 8
(B) 9
(C) 10
(D) 12
In the adjoining figure, $\mathrm{ABCD}$ is a quadrilateral. The bisectors of $\angle \mathrm{B}$ and the exterior angle at $\mathrm{D}$ meet at $\mathrm{P}$. Given $\angle \mathrm{C}=80^{\circ}, \angle \mathrm{ADC}=\frac{1}{2} \angle \mathrm{A}$ and $\angle \mathrm{A}=\angle \mathrm{C}+40^{\circ}$. Then $\angle \mathrm{DPB}$ is
(A) $50^{\circ}$
(B) $60^{\circ}$
(C) $70^{\circ}$
(D) $80^{\circ}$
The number of 3-digit number which contain 6 and 7 is
(A) 52
(B) 60
(C) 62
(D) 64
The difference between the biggest and the smallest three digit number each of which has different digits is
(A) 864
(B) 875
(C) 885
(D) 895
If $3 x+1=2 y-1=5 z+3=7 w+1=15$, the value of $6 x-3 y+5 z-8 w$ is
(A) 1
(B) 2
(C) 3
(D) None of these
Five years ago the average age of Aruna, Roy, David and salman is 45 years. Sita joins them now,. The average age of all the five now is 49 years. The present age of sita is (in years)
(A) 45
(B) 43
(C) 51
(D) 48
The fraction $\frac{B}{3 x-1}$ is subtracted from the fraction $\frac{A}{2 x+3}$. The resulting fraction is $\frac{-11}{(2 x+3)(3 x-1)}$. Then $A+B=$
(A) 11
(B) -11
(C) 5
(D) -5
There are some cows and ducks. The total number of legs is equal to 14 more than twice the number of heads. The number of cows is
(A) 5
(B) 6
(C) 7
(D) 8
The sum of $5 \%$ of a number and $9 \%$ another number is equal to sum of the $8 \%$ first number and $7 \%$ of the second number. The ratio between the numbers is
(A) $3: 2$
(B) $5: 7$
(C) $7: 9$
(D) $2: 3$
The length of two sides of an isosceles triangle are $8 \mathrm{~cm}$ and $14 \mathrm{~cm}$. The perimeter of the triangle (in $\mathrm{cm}$ ) is
(A) 30
(B) 36
(C) 19
(D) 30 or 36
There are three cell phones A, B, C. A is $50 \%$ costlier than C and B is $25 \%$ costlier than C.A is a $\%$ costlier than $\mathrm{B}$. Then $a=$
(A) 25
(B) 20
(C) 15
(D) 10
Sushant wrote a two digit number. He added 5 to the tens digit and subtracted 3 from the unit digit of the number and got a number equal to twice the original number. The original number is
(A) 47
(B) 74
(C) 37
(D) 73
The units digit of $5^{2018}-3^{2018}$ is
(A) 5
(B) 6
(C) 7
(D) 4
The smallest natural number that has to be added to 803642 to get a number which is divisible by 9 is $\rule{2cm}{0.15mm}$.
The greatest two digit number that will divided 398, 436, and 542 leaving respectively 7, 11 and 15 as remainders is $\rule{2cm}{0.15mm}$.
$\frac{2}{3}$ is $\rule{2cm}{0.15mm}$ of $\frac{1}{3}$.
The sum of 5 positive integers is 280. The average of the first 2 number is 40. The average of the third and fourth number is 60. The fifth number is $\rule{2cm}{0.15mm}$.
If $a: b=3: 4$ and $\frac{p}{q}=\frac{a^2+b^2+a b}{a^2+b^2-a b}$, where $p$, $q$ have no common divisors other than $1, p+q$ is $\rule{2cm}{0.15mm}$.
$a$ is a natural number such that a has exactly two divisors and $(a+1)$ has exactly three divisors. The number of divisors of $a+2$ is $\rule{2cm}{0.15mm}$.
The first term of a series is $\frac{2}{5}$. If $x$ is a term of this series, the next term is $\frac{1-x}{1+x}$. If $t_n$ denotes the $n$ th term and $t_{2018}-t_{2017}=\frac{p}{q}$, where $p$, $q$ are integers having no common factors other than $1, p+q$ is $\rule{2cm}{0.15mm}$.
In the adjoining figure, the side of the square is $\sqrt{\frac{2018}{\pi}} \mathrm{cm}$. The area of the unshaded region is $\left(\frac{\pi-2}{\pi}\right)$ A sq. cms. The value of $A$ is $\rule{2cm}{0.15mm}$.
$n$ is a natural number. The square root of the sum of the square of $n$ and 19 is equal to the next natural number to $n$. The value of $n$ is $\rule{2cm}{0.15mm}$.
Using only the digits 1,2, 4, 5, two- digit numbers are formed. The digits of the two digit number may be the same or different. The number of such two-digit number is $\rule{2cm}{0.15mm}$.
