For Class 7,8,9
Q1 ]. Perimeter of a rectangle is 15(3/7)m , if the length is 4(2/7)m , find its breadth .
Solution :
Given : Rectangle
Perimeter = P = 15(3/7)m = 108/7 m
Length = L = 4(2/7)m = 30/7m
Find Breadth = B = ?
P = 2( L + B)
108/7 = 2( 30/7 + B )
54/7 = 30/7 + B
54/7 – 30/7 = B
24/7 = B
3(3/7)m = B
Q2] . Rahul had a rope of 325(4/3)m long . He cut off a 150(3/5)m long piece ,then he divided the rest of the rope into 3 parts of equal length . Find the length of each part .
Solution : Total length of rope = 325(4/3)m = 979/3m
Length of rope cut off = 150(3/5)m = 753/5m
Therefore, remaining length of the rope = 979/3 – 753/5
L.C.M = 15
= (4895 – 2259) / 15
= 2636 / 15= 175.66m
Remaining length of rope = 175.66m or 176m
Divided into 3 equal parts
Length of each part = 176/3 = 58.6m or 59m
Q3]. If 3(1/2) litre of petrol costs Rs. 270(3/8), then find the cost of 4 litres of petrol ? .
Solution : Cost of 3(1/2) litre = Rs.270(3/8)
1] Cost of 1 litre = 270(3/8) ÷ 3(1/2)
= 2163 /8 ÷ 7/2
= 2163/8 x 2/7
= 309/4
2] Cost of each litre = Rs.309/4
Cost of 4 litre = ?
Thus, = 309/4 x 4
= Rs 309 is the cost of 4 litres of petrol .
Q4]. Ramesh earns Rs 40,000 per month. He spends 3/8 of the income on food , 1/5 of the remaining on LIC premium and then 1/2 of the remaining on other expenses . Find how much money is left with him .
Solution : Total monthly income = Rs 40,000
1] Expenditure on food = 3/8 of the income
= 3/8 x 40,000
= Rs.15,000
2] Remaining amount = 40,000 – 15,000 = Rs 25,000
3] Expense on LIC premium = 1/5 of the remaining
= 1/5 x 25,000
= Rs 5000
4] Remaining amount = 25,000 – 5000 = Rs 20,000
5] Other expenses = 1/2 of the remaining
= 1/2 x 20,000
= 10,000
Therefore , money left with him = 20,000 – 10,000
= Rs 10,000
Q5]. A, B , C , D and E went to a restaurant for dinner . A paid 1/2 of the bill, B paid 1/5 of the bill and the rest of the bill was shared equally by C , D and E . What fraction of the bill was paid by each ? .
Solution : Let the total amount of the bill = Rs 1
Given : A paid = 1/2 of the bill
= B paid = 1/5 of the bill
Therefore , remaining bill amount = 1 – ( 1/2 + 1/5 )
= 1 – ( 5+2)/10
= 1 – 7/10
= (10 – 7) / 10
= 3/10
Total number of person remaining = 3 ( i.e. C , D , E )
Remaining bill is shared equally among 3 persons
therefore, fraction of the bill paid by each is
= (3/10 ) / 3
= (3/ 10 ) x (1/ 3)
= ( 1/10 )
Q6]. 2/5 of the total number of students of a school come by the car while 1/4 of students come by bus to school . All the other students walk to school , of which 1/3 walk on their own and the rest are escorted by their parents . If 224 students come to school walking on their own , how many students study in the school ? .
Solution : Let the total number of students = x
Number of students come by car = 2/5 of x = 2x /5
Number of students come by bus = 1/4 of x = 1x/4
1] Number of students come by walking =
= x – ( 2x/5 + 1x/4 )
= x – (8x + 5x ) / 20
= x – 13x /20
= ( 20x – 13x )/ 20
= 7x /20
2] Total number of students come by their own = 224
Fraction of numebr of students come by their own = 1/3 of 7x 20
According to ques ,
= 1/3 x (7x) /20 = 224
= 7x / 60 = 224
= (224 x 60 ) / 7
= 1920 = x
Therefore , Number of students = x = 1920
Q7]. A mother and her two sons got a room constructed for Rs 60,000. The elder son contributes 3/8 of his mother’s , contribution while the younger son contributes 1/2 of his mother’s share . How much do the three contributes individually ?.
Solution : Total amount = Rs 60,000
Let mother’s contribution = Rs x
Therefore, elder son’s contribution = 3/8 of mother’s contribution
= 3/8 x
Therefore, younger son’s contribution = 1/2 of mother’s contribution
= 1/2 x
According to question
x + 3x/8 + x/2 = 60,000
(8x + 3x + 4x ) / 8 = 60,000
16 x / 8 = 60,000
x = ( 60,000 x 16 )/ 8
x = 32,000
Mother’s share = x = Rs 32,000
Elder son’s share = 3/2 x 32,000 = Rs 12000
Younger’s son’s share = 1/2 x 32000 = Rs 16000
Q8]. In a class of 56 students , the number of boys is 2/5th of the number of girls . Find the number of boys and girls ?.
Solution : Total students = 56
Let the number of girls = x
Therefore , the number of boys is = 2x/5
According to the question ,
x + 2x /5 = 56
5x + 2x / 5 = 56
7x /5 = 56
x = 56 x 5 / 7
x = 40 = Girls
Boys = 2/5 x 40 = 16
Q9] A man donated 1/10 of his money to a school , 1/6th of the remaining to a church and the remaining money he distributed equally among his thee children . If each child gets Rs 50,000 how much money did the man originally have ? .
Solution : Let the original amount be = Rs x
1] Amount donated to school = 1/10 of total amount
= Rs (1/ 10 )x
2] Remaining amount after giving to a school = x – x/10
= Rs 9x/10
3] Amount given to a church = 1/6 of Remaining
= 1/6 x 9x /10
= Rs 3x /20
4] Remaining amount after giving to a church = 9x /10 – 3x / 20
= (18x – 3x )/ 20
= Rs 3x/4
5] Amount given to 3 children equally = (3x/4) = (3x/4) x (1/3)
= Rs x/4
6] But given each share = 50,000
x /4 = 50,000
x = 2,00,000
Originally he had = 2,00,000
Q10]. If 1/4 of a number is added to 1/3of that , the result is 15 greater than half of that number . Find the number ? .
Solution : Let the number = x
1/4 of a number = x/4
1/3 of a number = x/3
According to question ,
x/4 + x/3 = x/2 + 15
(3x + 4x )/ 12 = x/2 + 15
7x/12 = x/2 + 15
7x/12 – x/2 = 15
(7x – 6x)/12 = 15
x /12 = 15
x = 180
Q11] . A student was asked to multiply a given number by 4/5 by mistake , he divided the given number by 4/5 . His answer is 36 more than the correct answer . What was the given number .
Solution : Let the given number = x
1] Wrong answer = (x/4 ) x 5 = 5x/4
2] Correct answer = ( x ) x 4/5 = 4x/5
According to the question ,
5x/4 – 4x/5 = 36
(25x – 16x ) / 20 = 36
9x / 20 = 36
x = 36 x 20 /9
x = 80