বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Let,
the number is 'x'
then ,
(1/3) × (1/4) × x = 15
⇒ x/12 = 15
⇒ x = 180
Now,
(3/10) × x = (3/10) × 180 = 18 × 3 = 54.
∴ three-tenths of that number is 54.
Solution:
We know that,
= a × a + 2ab + b × b
Now, (11.98 × 11.98 + 2 × 11.98 × 0.02 + 0.02 × 0.02) =
We can say that, (11.98 × 11.98 + 11.98 × Q + 0.02 × 0.02) will be a perfect square
if Q = 2 × 0.02 = 0.04
Solution:
Given,
7 people need to be served 1 cake
So, 98 people need to be served = 98/7 cakes
= 14 cakes
Solution:
x - 2 = 12 - 2 = 10
x/2 = 12/2 = 6
2/x = 2/12 = 1/6 ≈ 0.17
2 - x = 2 - 12 = - 10
The least value among the calculated options is - 10 or 2 - x
Solution:
Average = (0.36 + 4.6 + 0.64 + 2.4)/4
= 8.00/4
= 2.00
Solution:
13(x - 1) = 17(y - 1) .....(1)
⇒ 13x - 13 = 17y - 17
⇒ 13x + 4 = 17y
⇒ 4 = 17y - 13x
⇒ 4 - 4y = 13y - 13x
⇒ 4(1 - y) = 13(y - x)
Since x and y are integers, we know that (y - x) is an integer, which means 13(y - x) is a multiple of 13.
From this, we can conclude that 4(1 - y) is a multiple of 13
What is the smallest value of y (given that y is a positive integer greater than 1) such that 4(1 - y) is a multiple of 13?
If y = 14, then 4(1 - y) = 4(1 - 14) = 4(- 13) = - 52
So, y = 14 is the smallest value of y to meet the given conditions.
Now, putting the value of y = 14 in equation (1) we get,
13(x - 1) = 17(y - 1)
⇒ 13x - 13 = 17(14 - 1)
⇒ 13x = 17 × 13 + 13
⇒ 13x = 18 × 13
∴ x = 18
∴ x + y = 18 + 14 = 32