Exercise 7 B
Question 1
The greater of two numbers is 12 more than the smaller and the sum of the two numbers is 10 . Find the numbers.
Sol :
Question 2
One number is 5 times another. If 18 is subtracted from the greater, the remainder will be 3 times the smaller. Find the numbers.
Sol :
Question 3
(i) Find three consecutive numbers whose sum is $108 .$
(ii) Find three consecutive odd numbers whose sum is $93 .$
(iii) Find three consecutive even numbers whose sum is $246 .$
(iv) The sum of three consecutive multiples of 7 is 777 . Find these multiples.
Sol :
Question 4
Divide 534 into three parts such that the second part will be 32 less than twice the first, and the third will be 18 more than the first.
Sol :
Question 5
Three times the smallest of three consecutive odd numbers decreased by 7 equals twice the largest one. Find the numbers.
Sol :
Question 6
One number is 7 more than another and its square is 77 more than the square of the smaller number. What are the numbers ?
Sol :
Question 7
The square of the greater of two consecutive even numbers exceeds the square of the smaller by 36 . Find the numbers.
Sol :
Question 8
The denominator of a fraction is 3 more than the numerator. If 5 is added to both parts, the resulting fraction is equivalent to $\frac{4}{5}$. Find the fraction.
Sol :
Question 9
The difference between two positive integers is 50 and the ratio of these integers is $1: 3$. Find these integers.
Sol :
Question 10
The sum of the digits of a two-digit number is 7 . The number obtained by interchanging the digits exceeds the original number by 27 . Find the number.
Sol :
Question 11
Sushma is now 15 years older than Vijay but in 3 more years she will be 8 times as old as Vijay was 3 years ago. How old are they now ?
Sol :
Question 12
Sanjay is now $\frac{1}{2}$ as old as his brother. In 6 more years he will be $\frac{3}{5}$ as old as his brother then. What is the present age of each boy ?
Sol :
Question 13
(a) If the area is $3 x \mathrm{~cm}^{2}$, make an equation, and find $x$.
(b) If the perimeter is 40 cm, make an equation, and find $x$.
Sol :
Question 14
$4(x-2)$ metres of rope is used to fence the rectangular enclosure shown in the Fig. Find x.
Sol :
Question 15
Madhu's flower garden is now a square. If she enlarges it by increasing the width 1 metre and the length 3 metres, the area will be 19 sq metres more than the present area. What is the length of a side ?
Sol :
Question 16
The sides (other than hypotenuse) of a right triangle are in the ratio 3: 4. A rectangle is described on its hypotenuse, the hypotenuse being the longer side of the rectangle. The breadth of the rectangle is four-fifth of its length. Find the shortest side of the right triangle, if the perimeter of the rectangle is 180 cm
Sol :
Question 17
Two cars leave Delhi at the same time, travelling in opposite directions. If the average speed of one car is $5 \mathrm{~km} / \mathrm{hr}$ more than that of the other and they are $425 \mathrm{~km}$ apart at the end of $5 \mathrm{hrs}$, what is the average speed of each?
Sol :
Question 18
Two automobiles start out at the same time from cities $595 \mathrm{~km}$ apart. If the speed of one is $\frac{8}{9}$ of the speed of the other and if they meet in 7 hours, what is the speed of each ?
Sol :
Question 19
A motorboat goes downstream in a river and covers the distance between two coastal towns in five hours. It covers this distance upstream in six hours. If the speed of the stream is $2 \mathrm{~km} / \mathrm{h}$, find the speed of the boat in still water.
Sol :
Question 20
A steamer, going downstream in a river, covers the distance between two towns in 20 hours. Coming back upstream, it covers this distance in 25 hours. The speed of water is $4 \mathrm{~km} / \mathrm{h}$. Find the distance between the two towns.
Sol :
Question 21
Ranjana's mother gave her $₹ 245$ for buying New Year cards. If she got some 10 -rupee cards, $\frac{2}{3}$ as many 5 rupee cards, and $\frac{1}{5}$ as many 15 -rupee cards, how many of each kind did she buy ?
Sol :
Question 22
The enrolment in a school this year is $552 .$ This is an increase of $15 \%$ over last year's enrolment. How many were enrolled last year?
Sol :
Question 23
A fruit vendor buys some oranges at the rate of $₹ 5$ per orange. He also buys an equal number of bananas at the rate of ₹ 2 per banana. He makes a $20 \%$ profit on oranges and a $15 \%$ profit on bananas. At the end of the day, all the fruit is sold out. His total profit is $₹ 390$. Find the number of oranges purchased.
Sol :
Multiple Choice Questions (MCQs)
Question 24
A two digit number becomes five-sixth of itself when its digits are reversed. The two digits differ by 1 . The number is
(a) 45
(b) 54
(c) 56
(d) 65
Sol :
Question 25
The ratio of the present ages of two brothers is $1: 2$ and 5 years back the ratio was $1: 3$. What will be the ratio of their ages after 5 years ?
(a) $1: 4$
(b) $2: 3$
(c) $3: 5$
(d) $5: 6$
Sol :
Question 26
Two trains start from $P$ and $Q$ respectively and travel towards each other at a speed of $50 \mathrm{~km} / \mathrm{hr}$ and $40 \mathrm{~km} / \mathrm{hr}$ respectively. By the time they meet, the first train has travelled $100 \mathrm{~km}$ more than the second. The distance between $P$ and $Q$ is
(a) $500 \mathrm{~km}$
(b) $630 \mathrm{~km}$
(c) $660 \mathrm{~km}$
(d) $900 \mathrm{~km}$
Sol :
High Order Thinking Skills (HOTS)
Question 27
Nine persons went to a hotel for taking their meals. Eight of them spent $₹ 12$ each over their meals and the ninth spent $₹ 8$ more than the average expenditure of all the nine. What was the total money spent by them ?
Sol :
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