Further equations - class-VII

further equations

45 Questions Published

Questions

Question 1 Multiple Choice (Single Answer)

The ratio of the present age of Manoj to that of Wasim is $3:11$. Wasim is $12\ yr$ younger than Rehana. Rehanas age after $7\ yr$ will be $85\ yr$. What is thepresent age of Manojs father, who is $25\ yr$ older than Manoj?

  1. $43\ yr$
  2. $67\ yr$
  3. $45\ yr$
  4. $69\ yr$
Question 2 Multiple Choice (Single Answer)

The sum of three consecutive odd numbers is $38$ more than the average of these numbers. What is the first number

  1. $13$
  2. $17$
  3. $19$
  4. Data inadequate
  5. None of these
Question 3 Multiple Choice (Single Answer)

Solve $3x-450=2x-240$.

  1. $210$
  2. $230$
  3. $220$
  4. $200$
Question 4 Multiple Choice (Single Answer)

The age of  manoj  after $15$ years is $4$ times the age of that $15$ years before. His present age is 

  1. 10 years
  2. 15 years
  3. 20 years
  4. 25 years
Question 5 Multiple Choice (Single Answer)

The denominator of a rational number is greater from its numerators by 10. If the numerators is increased by 19 & the denominator is decreased by 1. The number obtained is $\dfrac { 3 }{ 2 } $. Find the rational number.

  1. $\dfrac{1}{11}$
  2. $\dfrac{7}{17}$
  3. $\dfrac{11}{21}$
  4. None of these
Question 6 Multiple Choice (Single Answer)

If
$\displaystyle \frac{a}{3y}, +, \frac{3b}{x}, =, 1$ and $3a + 1 = 2a + 2 $
x = 5, find the value of y.

  1. 0.83333
  2. 2.5
  3. 2.0
  4. 1.5
Question 7 Multiple Choice (Single Answer)

Given that $\displaystyle {\frac{-6p, -, 9}{3}, =, \frac{2p, +, 9}{5}},$ find the value of p

  1. -4
  2. -2
  3. 3
  4. 5
Question 8 Multiple Choice (Single Answer)

A boy is now $a$ years old and his father is $5a$ years old. How old will the father be when the boy is $3a$ years old? How old was the father when the boy was born?

  1. $7a, 4a$ years
  2. $4a, 10a$ years
  3. $12a, 3a$ years
  4. $15a, 3a$ years
Question 9 Multiple Choice (Single Answer)

A boy was asked to multiply a given number by $\displaystyle \frac{8}{17}$. Instead, he divided the given number by $\displaystyle \frac{8}{17}$ and got the result $225$ more than what he should have got if he had multiplied the number by $\displaystyle \frac{8}{17}$. The given number was

  1. $8$
  2. $17$
  3. $64$
  4. $136$
Question 10 Multiple Choice (Single Answer)

In a caravan  in addition to 50 hens there are 45 goats and 8 camels with some keepers.  If the total number of feet be 224 more then the number of heads in the caravan, find the number of keepers

  1. 5
  2. 8
  3. 10
  4. 15
Question 11 Multiple Choice (Single Answer)

The solution of $\displaystyle 2^{3x-6} =\frac{1}{8^x}$ is---

  1. 1
  2. $\displaystyle \frac{4}{2}$
  3. 4
  4. -1
Question 12 Multiple Choice (Single Answer)

Solve $1.32y + 0.02y = 1.19 + y$.

  1. $-\dfrac{7}{2}$
  2. $3\dfrac{1}{2}$
  3. $\dfrac{7}{4}$
  4. $-3\dfrac{1}{4}$
Question 13 Multiple Choice (Single Answer)

In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?

  1. $2$
  2. $3$
  3. $4$
  4. $5$
Question 14 Multiple Choice (Single Answer)

A number consists of two digits whose sum is $9$. If $27$ is added to the number, its digits are interchanged. Are the given steps to find the number true?
Step $1$: Let the unit's digit be x
Step $2$: Then, ten's digit $=(9-x)$
$\therefore$ number $=10\times (9-x)+x\Rightarrow 90-10x+x=(90-9x)$
Step $3$: Adding $27$ to the number $90-9x$ we get $117-9x$
Step $4$: Number with digits interchanged is $10x+(9-x)=9x+9$
Step $5$: $117-9x=9x+9$ 
Step $6$: Therefore unit's digit$=6$ and ten's digit $=3$
Step $7$: Hence the number $=36$.

  1. Yes
  2. No
  3. Cannot say
  4. Only step $1$ and $2$ are correct
Question 15 Multiple Choice (Single Answer)

When a number is reduced by $4$, it becomes $80%$ of itself. Find the number.

  1. $20$
  2. $30$
  3. $40$
  4. $50$
Question 16 Multiple Choice (Single Answer)

A number is multiplied by $2\displaystyle\frac{1}{3}$ times itself and then $61$ is subtracted from the product obtained. If the final result is $9200$, then the number is __________.

  1. $36$
  2. $63$
  3. $67$
  4. $37$
Question 17 Multiple Choice (Single Answer)

The two consecutive multiples of $3$ whose sum is $51$ are __________.

  1. $24, 27$
  2. $20, 31$
  3. $40, 11$
  4. $25, 26$
Question 18 Multiple Choice (Single Answer)

$\displaystyle\left(\displaystyle\frac{2}{3}\right)^{rd}$ of a number when multiplied by $\displaystyle\frac{3}{4}$ of the same number make $338$. The number is ___________.

  1. $18$
  2. $24$
  3. $36$
  4. $26$
Question 19 Multiple Choice (Single Answer)

A number is multiplied by half of itself and then $32$ is added to the product, if the final result is $130$, then find the original number.

  1. $4$
  2. $7$
  3. $5$
  4. $14$
Question 20 Multiple Choice (Single Answer)

If $\left(\displaystyle\frac{2}{3}\right)^{rd}$ of a number is $20$ less than the original number, then the number is ___________.

  1. $60$
  2. $40$
  3. $80$
  4. $120$
Question 21 Multiple Choice (Single Answer)

A lady reaches her office $20$ minutes late by traveling at a speed of $20$ km/h and reaches $15$ minutes early by traveling at $30$ km/h. By how much time will she be early or late if she travels at $25$ km/h?

  1. $1$ minute early
  2. $5$ minutes early
  3. $1$ minute late
  4. $5$ minutes late
Question 22 Multiple Choice (Single Answer)

The average age of $3$ sisters is $15$. If the ages of $2$ sisters are $12$ years and $15$ years, the age of the third sister is-

  1. 21 years
  2. 17 years
  3. 18 years
  4. 16 years
Question 23 Multiple Choice (Single Answer)

The difference of two numbers is $72$ and the quotient obtained by dividing one by the other is $3$. Find the numbers.

  1. $36$ $and$ $108$
  2. $16$ $and$ $88$
  3. $63$ $and$ $135$
  4. $\text{none}$
Question 24 Multiple Choice (Single Answer)

In an orchard, $\dfrac{1}{5}$ are orange trees, $\dfrac{3}{13}$ are mango trees and the rest are banana trees.  If the banana trees are $148$ in number, find the total number of trees in the orchard.

  1. $252$
  2. $360$
  3. $260$
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  4. $352$
Question 25 Multiple Choice (Single Answer)

At present anil is $1.5$ times of purvis age. $8\ yr$ later, the respective ratio between Anil and Purvis ages will be $25:18$. What is Purvis present age?

  1. $50\ yr$
  2. $28\ yr$
  3. $42\ yr$
  4. $36\ yr$
Question 26 Multiple Choice (Single Answer)

Solve for $x : \dfrac { x + 2 } { 6 } - \left[ \dfrac { 11 - x } { 3 } - \dfrac { 1 } { 4 } \right] = \dfrac { 3 x - 4 } { 12 }$

  1. $\dfrac { 6 } { 11 }$
  2. 10
  3. 14
  4. 11
Question 27 Multiple Choice (Single Answer)

Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. Find the number, if the difference between its digits is $3$. 

  1. $14$
  2. $25$
  3. $36$
  4. $47$
Question 28 Multiple Choice (Single Answer)

Solve: $\displaystyle \frac{2x, +,1}{10}, -, \frac{3, -, 2x}{15}, =, \frac{x, -, 2}{6}$.


Hence, find y, if $\displaystyle \frac{1}{x}, +, \frac{1}{y}, +, 1, = 0$.

  1. $\displaystyle x\, =\, -\frac{7}{5}; \, y\, =\, -\frac{7}{2}$
  2. $\displaystyle x\, =\, -\frac{2}{5}; \, y\, =\, \frac{7}{2}$
  3. $\displaystyle x\, =\, -\frac{6}{5}; \, y\, =\, -\frac{7}{2}$
  4. $\displaystyle x\, =\, -\frac{12}{5}; \, y\, =\, \frac{7}{2}$
Question 29 Multiple Choice (Single Answer)

An altitude of a triangle is five-third the length of its corresponding base. If the altitude is increased by $4 cm$ and the base is decreased by $2 cm$, the area of the triangle remains same. Find the base and the altitude of the triangle.

  1. The base of the triangle is $12 cm$ and altitude is $20 cm$.
  2. The base of the triangle is $4 cm$ and altitude is $34 cm$.
  3. The base of the triangle is $16 cm$ and altitude is $12 cm$.
  4. The base of the triangle is $8 cm$ and altitude is $32 cm$.
Question 30 Multiple Choice (Single Answer)

Neglecting air resistance, the upward velocity of the water in the stream of a particular fountain is given by the formula $v = -32t + 28$, where $t$ is the number of seconds after the water leaves the fountain. While going upward, the water slows down until at the top of the stream, the water has a velocity of $0$ feet per second. How long does it take a droplet of water to reach the maximum height?

  1. $0.825$ seconds
  2. $0.925$ seconds
  3. $0.875$ seconds
  4. $0.975$ seconds
Question 31 Multiple Choice (Single Answer)

Twelve years hence a person will be four times as he was twelve years ago, then his present age is

  1. $20$ years
  2. $25$ years
  3. $28$ years
  4. $30$ years
Question 32 Multiple Choice (Single Answer)

A father is at present three as old as his son . Five years back he was four times as old as his son.  Find the age of his son

  1. 12 years
  2. 15 years
  3. 18 years
  4. 20 years
Question 33 Multiple Choice (Single Answer)

If the sum of four consecutive even integers is $212$, what is the value of the second even integer?

  1. $50$
  2. $51$
  3. $52$
  4. $53$
Question 34 Multiple Choice (Single Answer)

If the sum of four consecutive odd integers is $400$, what is the value of the first odd integer?

  1. $95$
  2. $96$
  3. $97$
  4. $98$
Question 35 Multiple Choice (Single Answer)

If the sum of four consecutive integers is $110$, what is the value of the third consecutive integer?

  1. $26$
  2. $27$
  3. $28$
  4. $29$
Question 36 Multiple Choice (Single Answer)

The sum of a $2$ digit number and the number obtained by reversing its digits is $154$. If the digits differ by $4$, find the number.

  1. $95$
  2. $73$
  3. $84$
  4. $62$
Question 37 Multiple Choice (Single Answer)

Two numbers are in the ratio $3 : 5$. If $9$ is subtracted from each, the new numbers are in the ratio $12 : 23$. Find the smaller number.

  1. $27$
  2. $33$
  3. $49$
  4. $55$
Question 38 Multiple Choice (Single Answer)

The age of Vamsi's sister is $4\dfrac { 1 }{ 2 } $ times that of Vamsi, where as his uncle is $30$ years older than him. If the total of their ages is $56$ years, what is the age of Vamsi?

  1. $12$ years
  2. $10$ years
  3. $8$ years
  4. $4$ years
Question 39 Multiple Choice (Single Answer)

Deepak bought $12$ oranges for Rs $7.20$. Vimal bought x oranges more than Deepak's for Rs $9.60$. What is the value of x?

  1. $2$
  2. $5$
  3. $4$
  4. $6$
Question 40 Multiple Choice (Single Answer)

Pipes A and B can fill a tank in $18$ minutes and $12$ minutes respectively. If both the pipes are opened simultaneously, how long will they take to fill the tank?

  1. $30$ minutes
  2. $20$ minutes
  3. $10 $ minutes
  4. $7\dfrac{1}{5}$ minutes
Question 41 Multiple Choice (Single Answer)

The sum of three non-zero prime numbers is $100$. One of them exceeds the other by $36$. Find the largest number.

  1. $73$
  2. $91$
  3. $67$
  4. $57$
Question 42 Multiple Choice (Single Answer)

The sum of two numbers is $45$ and their difference is $11$. What are the two numbers?

  1. $28$ and $17$
  2. $27$ and $18$
  3. $25$ and $20$
  4. $22$ and $23$
Question 43 Multiple Choice (Single Answer)

The number of solution(s) of the equation $[x]+2{-x}=3x$, is$/$are (where $[]$ represents the greatest integer function and ${ x}$ denotes the fractional part of x$)$:

  1. $1$
  2. $2$
  3. $3$
  4. $0$
Question 44 Multiple Choice (Single Answer)

A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Which of the given steps is CORRECT to find the number?
Step 1 : Let the units digit be x
Step 2 : Then, ten's digit = (9 - x)
$\therefore$  Number = 10 x (9 - x) + x
$\Rightarrow$  90 - 10x + x = (90 - 9x)
Step 3 : Adding 27 to the number 90 - 9x, we get 117 - 9x
Step 4 : Number with digits interchanged is 10x + (9 - x) = 9x + 9
Step 5 : 117 - 9x = 9x + 9
Step 6 : Therefore unit's digit = 6 and ten's digit = 3
Step 7 : Hence the number = 36.

  1. Only Step 4
  2. Both Step 1 and Step 2
  3. Step 1, 2, 3 and 4
  4. All steps are correct
Question 45 Multiple Choice (Single Answer)

Peter's age in $10$ years will be $12$ less than $4$ times his current age. What is Peter's current age (in years)?

  1. $7.33$
  2. $7.71$
  3. $6.04$
  4. $6.49$