বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Given,
Man covers half of his journey at 12 km/h
The remaining half at 6 km/h
His average speed is = (2 × 12 × 6)/(12 + 6)
= 144/18 = 8 km/h
Solution:
Let, the two–digit number be = (10x + y) where x < y.
Number obtained on reversing the digits = (10y + x)
ATQ,
10y + x = 4 (10x + y) - 24
⇒ 40x + 4y - 10y - x = 24
⇒ 39x - 6y = 24
⇒ 13x - 2y = 8 ....(i)
Again, y - x = 7
y = x + 7 ....(ii)
⇒ 13x - 2 (x + 7) = 8
⇒ 13x - 2x - 14 = 8
⇒ 11x = 14 + 8 = 22
⇒ x = 22/11
∴ x = 2
From equation (ii),
y - 2 = 7
⇒ y = 2 + 7
∴ y = 9
So, Number = 10x + y = (10 × 2) + 9 = 29
Solution:
Suppose, a = 1 and b = 2
a + b = 1 + 2 = 3
ab + 1 = 1 × 2 + 1 = 3
=10
Solution:
Let the original number be x
ATQ,
{5(x + 7)/9} - 3 = 12
⇒ {5(x + 7) - 27}/9 = 12
⇒ 5(x + 7) - 27 = 108
⇒ 5x + 35 - 27 = 108
⇒ 5x + 8 = 108
⇒ 5x = 100
∴ x = 20
Solution:
Maximum daily wages of the officers = H.C.F of Tk. 4956 and Tk. 3894
H.C.F of 4956 & 3894 = 354
So, he was appointed for 4956/354 = 14 days
But he was present = 3894/354 = 11 days.
So, he was absent for (14 -11) days = 3 days
Solution:
Let the number be x
ATQ,
x - 12 = 20% of x
⇒ x - 12 = x/5
⇒ x - x/5 = 12
⇒ 4x/5 = 12
⇒ x = (12 × 5)/4
∴ x = 15
Solution:
Let the number be = a
The reciprocal of the number is = 1/a
According to the question,
a + (1/a) = 2
⇒ + 1 = 2a
⇒ - 2a + 1 = 0
⇒ = 0
∴ a = 1
Hence, the number = 1
