Sana and Ripa earn in the ratio 2: 1. They spend in the ratio 5: 3 and save in the ratio 4: 1. If the total monthly savings of both Sana and Ripa are Tk. 5,000, calculate the monthly income of Ripa.
Let, Sana earns 2x Tk. monthly ∴Ripa earns x Tk. monthly And again, Sana spends 5y Tk ∴Ripa spends 3y Tk According to question (2x - 5y) : (x - 3y) = 4:1
=2x-5yx-3y=41 =4x-12y=2x-5y =2x=7y ∴y=2x7
Again ((2x - 5y)) + (x - 3y) = 5000 = 3x - 8y = 5000 =3x-8×2x7=5000 =3x-16x7=5000 =21x-16x7=5000 =5x=5000×7 ∴x=7000 ∴Ripa earns 7,000 Tk. monthly.
A certain amount increases by 60% in six years at a simple interest rate. What will be the interest of Tk. 12,000 after 3 years at the same rate compounded annually?
Let, the principal is 100 Tk. After 6 years, the amount will be = 100 of 160% = 160Tk.
∴Simple interest = 160 - 100 = 60Tk . ∴1 year interest: 60 =606= 10 Tk. ∴Rate of interest = 10% ∴The amount of 12,000 Tk. for 3 years at 10% compounded annually is =12000(1+110)3=12000(1110)3=12000×1110×1110×1110=15972 Tk.
∴Required interest = 15 ,972-12,000=3,972 Tk.
In a square field of side 30 meters, 4 cows are grazing the field as they are tied at each of the four corners with a 14 meter long rope for each cow. What is the ungrazed area in the field?
Given, One side of the square = 30 m ∴Area of the square (30)2 m2 = 900 m2 ∴Area covered by the 4 cows in the over field=4×14πr2m2 =227×(14)2 m2 =(227×14×14) m2 =616 m2 ∴Ungrazed area=900-616=284m2
There are two examination rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A then the number of students in A is double the number of students in B. What is the number of students in room A?
Let, the number of students in rooms A and B be x and y respectively Then, x - 10 = y + 10 =x - y = 20 ..............(1) and x+20=2(y-20) =x - 2y =-60.......(ii) Solving (i) and (ii) we get: x = 100 v = 80. ans: The number of students in room A = 100
If m and n are whole numbers such that mn prime prime =121, then the value of (m - 1)(n + 1) is:
m2=121 বলে চেষ্টা করুন 121 কে বর্গ আকারে প্রকাশ করতে,
সেক্ষেত্রে mn=112 তাই m=11 এবং n=2
∴(m-1)n+1=(11-1)2+1=103=1000.