RBI Grade B Maths Questions Paper With Explanation, Download Maths PDF for Free

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Direction : Study the following questions carefully and choose the right answer.
Important for :
1
The road viz. NH-1 and NH-2 connecting two towns, A Kashmir Valley and B Leh, goes only uphill or downhill, i.e., there is no stretch of road that is level. Virat’s car goes at a constant speed of 40 km/hr uphill and 80 km/hr downhill. What is the distance between Kashmir Valley and Leh, if it takes exactly 9 hours for Virat to make one round trip from Kashmir Valley and Leh and back?
» Explain it
A
Let the road from Kashmir Valley to Leh be downhill for a distance of x km, and uphill for a distance of (S – x) km. (Where S = distance between the two towns). 
 
Now, on the return journey (S – x) km will be downhill and x km will be uphill. 
 
Hence total distance downhill = x + (S – x) = S 
 
And total distance uphill = (S – x) + x = S 
 
Hence, total time =  S  +  S  = 9 hour (Given)
40 80

⇒ (2 × S + S) = (80 × 9) 
 
⇒ 3 × S = (80 × 9) 

⇒ S =  ( 80 ×  9 )  = 240
3

Thus, the distance between Kashmir Valley and Leh = 240 km

Hence, option (A) is correct.
 
2
Raghuram Rajan deposited Rs.20000 on 1st January 2017 to open a savings account. He withdrew Rs.1,000 on the 10th of every month. He closed the account on 6th June 2017. If the bank pays interest at 4% p.a., then approximately how much interest did he receive on closing the account?
» Explain it
C
The interest I on principle P for D days at R% p.a. is given as
I = P × D × 2R
73000

From 1st January to 9th January,

P = Rs.20000, D = 9 and R = 4% p.a.
 
Therefore, interest, I1 =  20000 × 9 × 8  =  1440000  = Rs. 19.73
73000 73000

From 10th January to 9th February,

P = Rs.19000, D = 31 and R = 4% p.a.
 
Therefore, interest, I2 =  19000 × 31 × 8  =  4712000  = Rs. 64.55
73000 73000

From 10th February to 9th March,

P = Rs.18000, D = 28 and R 4% p.a.
Therefore, interest, I3 =  18000 × 28 × 8  =  4032000  = Rs. 55.23
73000 73000

From 10th March to 9th April,

P = Rs.17000, D = 31 and R = 4%p.a
 
Therefore, interest, I4 =  17000 × 31 × 8  =  4216000  = Rs. 57.75
73000 73000

From 10th April to 9th May,

P = Rs.16000, D = 30 and R = 4% P.a.
 
Therefore, interest, I5 =  16000 × 30 × 8  =  3840000  = Rs. 52.60
73000 73000

From 10th May to 6th June,

P = Rs.15000, D = 27 and R = 4% p.a.
The days are 27 as on the day of closing he will not get the interest. So 22 days of May and 5 days of June will be counted.
Therefore, interest, I6 =  15000 × 27 × 8  =  3240000  = Rs. 44.38
73000 73000

Total Interest- = I1 + I2 + I3 + I4 + I5 + I6 = 19.73 + 64.55 + 55.23+ 57.75 + 52.60 + 44.38

= Rs.294.24 = Rs.294 approximately

Hence, option (C) is correct.
 
3
Aman borrowed a sum of money from Rohan at 10% rate per annum for 4 years at simple interest. Due to some reason Aman was unable to pay that amount in that period. Due to this Rohan took simple interest for that stipulated period (for 4 years) and after that the interest was compounded annually at same rate from the next year. The sum of money was returned after 7 years. As a result, Aman has to pay 3268 more to Rohan. Find the sum of money borrowed by Aman?
» Explain it
D
Let money borrowed by Aman is x.

If Rohan didn’t apply compound interest, amount payable by Aman after 7 years is.

x +  x × 7 × 10  =  17x
100 10

Now Rohan applied SI for first 4 years and for remaining 3 years CI is applicable, then amount payable by Aman is.

For first 4 years.

x +  x × 4 × 10  =  14x
100 10

For next 3 year CI is payable

∴  14x ( 1 +  10 ) 3  =  18634x
10 100   10000

Now Aman has to pay 3268 more.

∴  18634x  –  17x  = 3268
10000 10

∴  1634x  = 3268
10000

x = 20000

Hence, option D is correct.
4
Jethalal and Tarak Mehta have two spools of 'Dhaga' (a specially prepared thread) to fly their kites. Each of the Dhagas has tiny knots at regular intervals, which helps in keeping track of the length of the Dhaga that is used. Each of the persons has the same length of Dhaga. While Jethalal'sDhaga has knots at intervals of 10 feet, Tarak Mehta's Dhaga has knots at intervals of 12 feet. Also, Tarak Mehta's Dhaga has exactly 10 knots less than that of Jethalal. If each of the Dhagas starts and ends with a knot, find the length (in feet) of the Dhaga with either of them.
» Explain it
B
Let Jethalal make n knots. Tarak Mehta makes (n – 10) knots. Since both the Dhagas start and end with a knot, the length of the Dhaga L given by
 
L = 10(n – 1) =12 (n – 11)
 
⇒ n = 61 and L = 600

Hence, option (B) is correct.
 
5
Prem Kumar had some currency notes of denominations Rs.50, Rs.20 and Rs.10, such that at least two notes of each denomination were present with him He had to pay a bill of Rs.200 in Big Bazaar and when he counted all the money he had, he realized that he was short of Rs.30. How many notes did Prem Kumar have?
» Explain it
A
Let the number or notes of denominations Rs.50, Rs.20 and Rs.10
 
with Prem Kumar be x, y and z respectively.
 
Total money with Prem Kumar = (200 – 30) = 170
 
(50x + 20y +10z) = 170.
 
Since x, y, z > 1, x cannot be 3 therefore x = 2.
 
When x = 2, y can be only 2 otherwise if y = 3, then x Will be equal to 1, which is not possible.
 
Therefore x = 2, y = 2 and z = 3.
 
The total number of notes with Prem Kumar is 7.
 
Alternative Solution:
 
We can directly start with two notes of each denomination, which gives us 100 + 40 + 20 = Rs.160. Now, the only possibility of
having exactly Rs.170 is to have just one additional note of Rs.10. 
 
Hence, 7 notes.

Therefore, option (A) is correct.