Concept of “Approximate Values” [सन्निकट मान]-02

1. Q: 2070.50 ÷ 15.004 + 39.001 × (4.999)² =?  [Ans. (e) 1113]

(a)  1005    (b) 997      (c) 1049     (d) 1213      (e) 1113

2. Q: (1223.9975)^1/2 =? [Ans. (c) 34]               

(a)  110    (b) 144    (c) 34     (d) 12.55     (e) 125

3. Q: {(20800)^1/2}^1/2 =? [Ans. (a) 12]     

(a)  12     (b) 120    (c) 140   (d) 102      (e) 1020

4. Q: 85.147 + 34.912 × 6.2 +? = 802.293 [Ans. (e) 500]                            

(a) 400 (b) 450 (c) 550 (d) 600 (e) 500

Solution: 

Detailed Explanation:

Concept: When we divide a number by any number, then we multiply both the numbers by 2 if they have 5 at the unit places. Even, if only divisor contains 5 at the unit place, then we multiply both the numbers by also.

For example, 275÷25 = 550÷50 = 55÷5 = 110÷10 = 11

Also, 312÷25 = 612÷50 = 1224÷100 = 12.24

1. Sol: 2070.50 ÷ 15.004 + 39.001 ´ (4.999)²

= 2×2070.50 ÷ 15.004×2 + (40-1) ×25

≡ 2×2070.50 ÷ 30 + 1000-25

≡ 2×207.050 ÷ 3.0 + 1000-25

≡ 2×207 ÷ 3 + 1000-25

≡ 2×69 + 1000-25

≡ 138 + 1000-25

≡ 113 + 1000

≡ 1113. Ans.

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Concept:

25² = (2×3) ×100 + 25 = 625

35² = (3×4) ×100 + 25 = 1225

45² = (4×5) ×100 + 25 = 2025

55² = (5×6) ×100 + 25 = 3025 and so on.

  

2. Sol: Since 1223.9975 ≡ 1224 ≡ 1225 ≡ 35²

So, (1223.9975)^1/2 = 35 ≡ 34. Ans.

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Concept: When we have to find the square root of any number, then we find two consecutive squares in between it lies.

3. Sol: Since, 19600 < 20800 < 22500

196 < 208 < 225

Or, 14² < 208 < 15²

So, 140² < 20800 < 150²

 It means that (20800)^1/2 lies between 140 and 150

140² = 19600

145² = 21025

150² = 22500

20800 is slight less than 145² (= 21025)

So, (20800)^1/2 = 143 or 144, which is again equal to 12²

Therefore, {(20800)^1/2}^1/2 ≡ {143 or 144}^1/2 = 12. Ans.

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4. Sol. 85.147 + 34.912 ´ 6.2 +?  = 802.293

Or, 85 + 35 × (6 + 0.2) +? = 802

Or, 85 + 210 + 7 +? = 802

Or, 302 +? = 802

Or? = 500. Ans.

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