Let the addition of two sums be x .
First sum = 48
∴ 8/ (8+13) × x = 48
⇒ (8/21) x = 48
⇒ x = 126 INR
CTET Maths MCQ - Algebra
Given, ratios are 1/2, 2/5 and 3/4.
∴ LCM(2,5, 4) = 20
⇒ 1/2 = 1/2 × 10/10 = 10/20,
2/5 = 2/5 × 4/4 = 8/20
and 3/4 = 3/4 × 5/5 = 15/20.
Clearly, 8/20<10/20<15/20 =2/5<1/2<3/4.
so, 2:5<1:2<3:4
Let a/b = b/c = c/d =k.
⇒ a=bk=ck2=dk3, b=dk2 and c=dk.
(b3 + c3 + d3 ) / (a3 + b3 + c3 ) = [(dk2)3 + (dk)3 + d3 ]/ [(dk3)3 + (dk2)3 + (dk)3 ]
=d3 [ K6 + K3 +1] / d3 [K9 + K6 + K3 ]
=[ K6 + K3 +1]/K3 [ K6 + K3 +1]
=1/K3 =1/a/d =d/a
⇒ a=bk=ck2=dk3, b=dk2 and c=dk.
(b3 + c3 + d3 ) / (a3 + b3 + c3 ) = [(dk2)3 + (dk)3 + d3 ]/ [(dk3)3 + (dk2)3 + (dk)3 ]
=d3 [ K6 + K3 +1] / d3 [K9 + K6 + K3 ]
=[ K6 + K3 +1]/K3 [ K6 + K3 +1]
=1/K3 =1/a/d =d/a
(4) Let number of 1 Rs,50 paise and
25 paise coins be 2.5x, 3x and 4x,
respectively.
Value of 1 Rs coins = 1 x 2.5x= 2.5x Rs.
Value of 50 paise coins = 0.50 x 3x.
=1.5x Rs.
Value of 25 paise coins = 0.25 x 4x.
=lx Rs,
Total value = 210 Rs.
⇒2.5x + 1.5x + 1x =210 => 5x = 210
⇒X= 42
Thus, number of 1 Rs coins= 2.5x
= 2.5 x 42 = 105
