২৩২২১
The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member?
উত্তর
40 years
সমাধান
Hints: Let, 4 years ago 9 person total age = x
Now, Increase age of 10 member with old man = 10 × 4 = 40
Total present age of 10 member = x + 40
Again let present age of younger member = y
Total present age of 10 new member = x + y
According to question.
x + 40 / 10 = x + y/ 10
x + 40 = x + y
y = 40
Age of younger member = 40
২৩২২২
The product of two numbers x and y is twice the sum of the numbers. What is the sum of the reciprocals of x and y?
উত্তর
1/2
সমাধান
Hints : xy = 2 ( x + y)
xy/ x + y = 2
x + y/xy = 1/2
1/x + 1/y = 1/2
২৩২২৩
The least number of 4 digits which is a perfect square, is:
উত্তর
1024
সমাধান
we know, least 4 digit numbers is 1000
we get ,√1000 = 31.62
So , least 4 digit numbers that perfect square is 32^2 = 1024
ans: 1024
২৩২২৪
The average of 7 consecutive number is 20. The largest of these numbers is:
উত্তর
23
সমাধান
Hints: The average of seven consecutive number is -
a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6/7 = 20
7a + 21 = 20 × 7
7a = 140 - 21
a = 119/7 = 17
Target = 17 + 6 = 23 (ans)
২৩২২৫
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
উত্তর
54
সমাধান
Hints: ধরি সংখ্যটি, x
তাহলে, 1/3 × 1/4 × x = 15
x = 180
180 × 3/10 = 54 (ans)
২৩২২৬
The sum of two positive integers multiplied by the bigger number is 204, and their difference multiplied by the smaller number is 35. The numbers are:
উত্তর
12, 5
সমাধান
Hints: এই ম্যথটি করলে উত্তর দেখে করলে দ্রুত হয়। প্রশ্নমতে দুইটি সংখ্যাকে যোগ করে বড় সংখ্যা দিয়ে গুন করলে 204 হয়। প্রথম উত্তর দিয়ে = (12 + 5) × 12 = 204 মিলে গেছে। বাকি গুলা যদি না মেলে তাহলে এাটই উত্তর।
২৩২২৭
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, Then how old is B?
উত্তর
10
সমাধান
Hints: ধরি, A, B, C এর বয়স A, B, C
তাহলে, B = 2C ; A = B + 2 = 2C + 2
এখন, A + B + C = 27
2C + 2 + 2C + C = 27
5C = 25
C = 5
B = 2C = 2 × 5 = 10
২৩২২৮
If 35% of a number is 12 less than 50% of that number, then the number is:
উত্তর
80
সমাধান
Hints: ধরি সংখ্যটি x
তাহলে, 35x/100 = 50x/100 - 12
35x - 50x = - 1200
15 x = 1200
x = 80
২৩২২৯
If selling price is doubled, The profit triples. Find the profit percent.
উত্তর
100
সমাধান
Hints:ধরি, cost price x এবং sell price y
তাহলে, 3(y - x) = (2y - x)
y = 2x
profit = (y - x) = (2x - x) = x
profit % = (x/x × 100%) = 100%
২৩২৩০
The ratio of three numbers is 3: 4: 5 and the sum of their squares is 1250. The sum of the numbers is:
উত্তর
60
সমাধান
Hints: ধরি, সংখ্যাগুলো 3x, 4x, 5x
এখন, (3x)2 + (4x)2 + (5x)2 = 1250
50x2 = 1250
x2 = 25
x = 5
তাহলে, sum = 3x + 4x + 5x = 12x = 12 × 5 = 60