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 45. 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 12 as old as his brother. In 6 more years he will be 35 as old as his brother then. What is the present age of each boy ?
Sol :
Question 13
(a) If the area is 3x cm2, 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 km/hr more than that of the other and they are 425 km apart at the end of 5hrs, what is the average speed of each?
Sol :
Question 18
Two automobiles start out at the same time from cities 595 km apart. If the speed of one is 89 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 km/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 km/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, 23 as many 5 rupee cards, and 15 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 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is
(a) 500 km
(b) 630 km
(c) 660 km
(d) 900 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 :
No comments:
Post a Comment