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What will come in place of the question mark (?) in the following number series?
4, 14, 48, 174, ?
4 × 1+10 × 1 = 14 14 × 2+10 × 2 = 48 48 × 3+10 × 3 = 174 So, 174 × 4+10 × 4 = 736
In how many different ways can the letters of the word ‘EQUATION’ be arranged so that the vowels always come together?
The word ‘EQUATION’ contains 8 different letters. When the vowels EUAIO are always together, they can be supposed to form one letter. Then, we have to arrange the letters QTN (EUAIO). Now, 4 letters can be changed in 4! = 24 ways. The vowels (EUAIO) can be arranged themselves in 5! = 120 ways. Required numbers of ways = (24 ×120) = 2880.
Priyal had three notebooks Yellow, Pink, White. of these, Yellow had 150 pages. Pink had 10% more pages and White had 10% less pages than Yellow pages. If she tore roughly 4%, 8% and 12% of pages in Yellow, Pink and White respectively, then what percent of pages did she tear out?
The income of Amit and Bhavya are in the ratio 5:3. The expenses of Amit, Bhavya and Chirag are in the ratio 5: 4 : 2. If Chirag spends Rs 2000 and Bhavya saves Rs. 800, then Amit saves
Let the incomes of Amit and Bhavya be Rs. 5x5x and Rs. 3x respectively. Let the expenses of Amit, Bhavya and Chirag be Rs. 5y, Rs. 4y and Rs. 2y respectively. Then, 2y = 2000 y = 1000 Bhavya saves = Rs. 800 3x – 4y = 800 3x - 4000 = 800 3x = 800 + 4000 = 4800 x = 1600 Amit’ saving = Rs. ( 5x5x —5y) = Rs. (5 × 1600 − 5 × 1000) = Rs. (8000—5000) Amit’ saving = Rs. 3000
A shopkeeper sold 12 wrist watch at a profit of 20% and 8 wrist watch at a profit of 15%. If he had sold all the 20 wrist watch at a profit of 15%, then his profit would have been reduced by Rs. 300 What is the cost price of each wrist watch?
In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
I. 6X + 9Y = 215
II. 16X – 18Y = -38
6X + 9Y = 215…………(i) 16X – 18Y = -38 Or 8X – 9Y = -19………………..(ii) Adding question (i) and (ii) 6X + 9Y + 8X – 9Y = 215 – 19 14X = 196 X = 14 6(14) + 9Y = 215 9Y = 131 Y = 14.5 and X = 14
I. X2 − 33X + 272 = 0
II. Y2 − 29Y + 204 = 0
X2 − 33X + 272 = 0 From equation (i) (X - 16) (X - 17) = 0 X = 16, 17 Y2 − 29Y + 204 = 0 From equation (ii) (Y - 12) (Y - 17) = 0 Y = 12, 17
I. 49X2 − 49X − 78 = 0
II. 56Y2 − 167Y + 102 = 0
I. X2 − 28X + 195 = 0
II. Y2 − 34Y + 285 = 0
I. 15X2 − 41X + 14 = 0
II. 3Y2 − 29Y + 56 = 0
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